# Publications

### 2024

We propose and experimentally demonstrate a general method allowing us to unravel microscopic noise events that affect a continuous quantum variable. Such unraveling is achieved by frequent measurements of a discrete variable coupled to the continuous one. The experimental realization involves photons traversing a noisy channel. There, their polarization, whose coupling to the photons' spatial wave packet is subjected to stochastic noise, is frequently measured in the quantum Zeno regime. The measurements not only preserve the polarization state, but also enable the recording of the full noise statistics from the spatially resolved detection of the photons emerging from the channel. This method proves the possibility of employing photons as quantum noise sensors and robust carriers of information.

Sub-wavelength arrays of atoms exhibit remarkable optical properties, analogous to those of phased array antennas, such as collimated directional emission or nearly perfect reflection of light near the collective resonance frequency. We propose to use a single-sheet sub-wavelength array of atoms as a switchable mirror to achieve a coherent interface between propagating optical photons and microwave photons in a superconducting coplanar waveguide resonator. In the proposed setup, the atomic array is located near the surface of the integrated superconducting chip containing the microwave cavity and optical waveguide. A driving laser couples the excited atomic state to Rydberg states with strong microwave transition. Then the presence or absence of a microwave photon in the superconducting cavity makes the atomic array transparent or reflective to the incoming optical pulses of proper frequency and finite bandwidth.

Atoms falling into a black hole (BH) through a cavity are shown to enable coherent amplification of light quanta powered by the BH-gravitational vacuum energy. This process can harness the BH energy towards useful purposes, such as propelling a spaceship trapped by the BH. The process can occur via transient amplification of a signal field by falling atoms that are partly excited by Hawking radiation reflected by an orbiting mirror. In the steady-state regime of thermally equilibrated atoms that weakly couple to the field, this amplifier constitutes a BH-powered quantum heat engine. The envisaged effects substantiate the thermodynamic approach to BH acceleration radiation.

### 2023

*2023 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2023*. Abstract

In recent works, we have put forth and experimentally demonstrated several novel schemes [1-5] for the detection of quantum noise signatures by exploiting frequent photonic measurements, allowing us to reach unprecedented, ultrahigh sensitivity to quantum noise.

We propose heat machines that are nonlinear, coherent, and closed systems composed of few field (oscillator) modes. Their thermal-state input is transformed by nonlinear Kerr interactions into nonthermal (non-Gaussian) output with controlled quantum fluctuations and the capacity to deliver work in a chosen mode. These machines can provide an output with strongly reduced phase and amplitude uncertainty that may be useful for sensing or communications in the quantum domain. They are experimentally realizable in optomechanical cavities where photonic and phononic modes are coupled by a Josephson qubit or in cold gases where interactions between photons are transformed into dipole-dipole interacting Rydberg atom polaritons. This proposed approach is a step toward the bridging of quantum and classical coherent and thermodynamic descriptions.

We examine spin excitation or polarization transfer via spin chains with long-range exchange interactions in the presence of diagonal and off-diagonal disorder. To this end, we determine the mean localization length of the single-excitation eigenstates of the chain for various strengths of the disorder. We then identify the energy eigenstates of the system with large localization length and sufficient support at the chain boundaries that are suitable to transfer an excitation between the sender and receiver spins connected to the opposite ends of the chain. We quantify the performance of two transfer schemes involving weak static couplings of the sender and receiver spins to the chain, and time-dependent couplings realizing stimulated adiabatic passage of the excitation via the intermediate eigenstates of the chain which exhibits improved performance.

### 2022

The quantum Zeno and anti-Zeno paradigms have thus far addressed the evolution control of a quantum system coupled to an immutable bath via non-selective measurements performed at appropriate intervals. We fundamentally modify these paradigms by introducing, theoretically and experimentally, the concept of controlling the bath state via selective measurements of the system (a qubit). We show that at intervals corresponding to the anti-Zeno regime of the system-bath exchange, a sequence of measurements has strongly correlated outcomes. These correlations can dramatically enhance the bath-state purity and yield a low-entropy steady state of the bath. The purified bath state persists long after the measurements are completed. Such purification enables the exploitation of spin baths as long-lived quantum memories or as quantum-enhanced sensors. The experiment involved a repeatedly probed defect center dephased by a nuclear spin bath in a diamond at low-temperature. The existing paradigms of system-bath control typically assume that the bath state is unchanged. By using spin defects in diamond, Dasari et al. demonstrate a scheme for controlling the state of the nuclear spin bath via selective measurements of the central qubit as a way of extending the qubit coherence time.

Our goal in this article is to elucidate the rapport of work and information in the context of a minimal quantum-mechanical setup: a converter of heat input to work output, the input consisting of a single oscillator mode prepared in a hot thermal state along with a few much colder oscillator modes. The core issues we consider, taking account of the quantum nature of the setup, are as follows: (i) How and to what extent can information act as a work resource or, conversely, be redundant for work extraction? (ii) What is the optimal way of extracting work via information acquired by measurements? (iii) What is the bearing of information on the efficiency-power tradeoff achievable in such setups? We compare the efficiency of work extraction and the limitations of power in our minimal setup by different, generic, measurement strategies of the hot and cold modes. For each strategy, the rapport of work and information extraction is found and the cost of information erasure is allowed for. The possibilities of work extraction without information acquisition, via nonselective measurements, are also analyzed. Overall, we present, by generalizing a method based on optimized homodyning that we have recently proposed, the following insight: extraction of work by observation and feedforward that only measures a small fraction of the input is clearly advantageous to the conceivable alternatives. Our results may become the basis of a practical strategy of converting thermal noise to useful work in optical setups, such as coherent amplifiers of thermal light, as well as in their optomechanical and photovoltaic counterparts.

We experimentally demonstrate, for the first time, noise diagnostics by repeated quantum measurements, establishing the ability of a single photon subjected to random polarization noise to diagnose non-Markovian temporal correlations of such a noise process. Both the noise spectrum and temporal correlations are diagnosed by probing the photon with frequent (partially) selective polarization measurements. We show that noise with positive temporal correlations corresponds to our single photon undergoing a dynamical regime enabled by the quantum Zeno effect (QZE), whereas noise characterized by negative (anti) correlations corresponds to regimes associated with the anti-Zeno effect (AZE). This is the first step toward a novel noise spectroscopy based on QZE and AZE in single-photon state probing able to extract information on the noise while protecting the probe state, a conceptual paradigm shift with respect to traditional interferometric measurements.

A minimal model of a quantum thermal machine is analyzed, where a driven two level working medium (WM) is embedded in an environment (reservoir) whose spectrum possesses bandgaps. The transition frequency of the WM is periodically modulated so as to be in alternating spectral overlap with hot or cold reservoirs whose spectra are separated by a bandgap. Approximate and exact treatments supported by analytical considerations yield a complete characterization of this thermal machine in the deep quantum domain. For slow to moderate modulation, the spectral response of the reservoirs is close to equilibrium, exhibiting sideband (Floquet) resonances in the heat currents and power output. In contrast, for faster modulation, strong-coupling and non-Markovian features give rise to correlations between the WM and the reservoirs and between the two reservoirs. Power boost of strictly quantum origin ('quantum advantage') is then found for both continuous and segmental fast modulation that leads to the anti-Zeno effect of enhanced spectral reservoir response. Such features cannot be captured by standard Markovian treatments.

The consensus regarding quantum measurements rests on two statements: (i) von Neumann's standard quantum measurement theory leaves undetermined the basis in which observables are measured, and (ii) the environmental decoherence of the measuring device (the "meter") unambiguously determines the measuring ("pointer") basis. The latter statement means that the environment (measures) observables of the meter and (indirectly) of the system. Equivalently, a measured quantum state must end up in one of the "pointer states" that persist in the presence of the environment. We find that, unless we restrict ourselves to projective measurements, decoherence does not necessarily determine the pointer basis of the meter. Namely, generalized measurements commonly allow the observer to choose from a multitude of alternative pointer bases that provide the same information on the observables, regardless of decoherence. By contrast, the measured observable does not depend on the pointer basis, whether in the presence or in the absence of decoherence. These results grant further support to our notion of Quantum Lamarckism, whereby the observer's choices play an indispensable role in quantum mechanics.

The control of open quantum systems and their associated quantum thermodynamic properties is a topic of growing importance in modern quantum physics and quantum chemistry research. This unique and self-contained book presents a unifying perspective of such open quantum systems, first describing the fundamental theory behind these formidably complex systems, before introducing the models and techniques that are employed to control their quantum thermodynamics processes. A detailed discussion of real quantum devices is also covered, including quantum heat engines and quantum refrigerators. The theory of open quantum systems is developed pedagogically, from first principles, and the book is accessible to graduate students and researchers working in atomic physics, quantum information, condensed matter physics, and quantum chemistry.

### 2021

We propose a novel principle of operating heat machines in a fully unitary (coherent) fashion by mixing few hot and cold thermal field modes in nonlinear interferometers. Such devices, specifically, interferometers containing Kerr-nonlinear intermode cross-couplers, are shown to enable autonomous concentration of the energy predominantly in a desired output mode, at the expense of the other modes. Their phase-coherent operation is reversible and it is approximately reversible even if intermode entanglement is neglected. Such few-mode coherent heat machines radically depart from the existing thermodynamic paradigm which treats heat machines as open systems dissipated by heat baths.

We put forward the concept of work extraction from thermal noise by phase-sensitive (homodyne) measurements of the noisy input followed by (outcome-dependent) unitary manipulations of the postmeasured state. For optimized measurements, noise input with more than one quantum on average is shown to yield heat-to-work conversion with efficiency and power that grow with the mean number of input quanta, the efficiency and the inverse temperature of the detector. This protocol is shown to be advantageous compared to common models of information and heat engines

We study the difference between the energy transfer rate and the engine efficiency with a microscopic model, widely used in the theoretical description of solar cells, as well as in light-harvesting systems. We show no violation of the second law of thermodynamics by correctly assessing the useful output work, even with the simple model treating the later work conversion as a simple “sink”.

We put forward a unified thermodynamic analysis of generic minimal models of solar-powered cyclic processes that can be viewed as quantum heat engines. The resulting general efficiency bound for work production is consistent with the second law of thermodynamics if it allows for heat and entropy generation. This bound is shown to interpolate between the Carnot and the Shockley–Queisser bounds. Power boost induced by coherence or multiexciton generation does not affect the efficiency. These features may allow us to design solar-pumped schemes that are optimal, both energetically and operationally.

### 2020

Characterization of microstructures in living tissues is one of the keys to diagnosing early stages of pathology and understanding disease mechanisms. However, the extraction of reliable information on biomarkers based on microstructure details is still a challenge, as the size of features that can be resolved with noninvasive magnetic resonance imaging (MRI) is orders of magnitude larger than the relevant structures. Here we derive from quantum information theory the ultimate precision limits for obtaining such details by MRI probing of water-molecule diffusion. We show that currently available MRI pulse sequences can be optimized to attain the ultimate precision limits by choosing control parameters that are uniquely determined by the expected size, the diffusion coefficient, and the spin relaxation time T-2. By attaining the ultimate precision limit per measurement, the number of measurements and the total acquisition time may be drastically reduced compared to the present state of the art. These results are expected to open alternative avenues towards unraveling diagnostic information by quantitative MRI.

We reveal the potentially important role of a general mechanism in quantum heat management schemes, namely, spectral filtering of the coupling between the heat baths in the setup and the quantum system that controls the heat flow. Such filtering is enabled by interfaces between the system and the baths by means of harmonic-oscillator modes whose resonant frequencies and coupling strengths are used as control parameters of the system-bath coupling spectra. We show that this uniquely quantum-electrodynamic mechanism, here dubbed bath spectral filtering, boosts the performance of a minimal quantum heat manager comprised of two interacting qubits or an analogous optomechanical system, allowing this device to attain either perfect heat diode action or strongly enhanced heat transistor action.

The occurrence of any physical process is restricted by the constraints imposed by the laws of thermodynamics on the energy and entropy exchange involved. A prominent class of processes where thermodynamic constraints are crucial involve polarization of nuclear spin baths that are at the heart of magnetic resonance imaging, nuclear magnetic resonance (NMR), quantum information processing. Polarizing a spin bath, is the key to enhancing the sensitivity of these tools, leading to new analytical capabilities and improved medical diagnostics. In recent years, significant effort has been invested in identifying the far-reaching consequences of quantum modifications to classical thermodynamics for such processes. Here we focus on the adverse role of quantum correlations (entanglement) in the spin bath that can impede its cooling in many realistic scenarios. We propose to remove this impediment by modified cooling schemes, incorporating probe-induced disentanglement or, equivalently, alternating non-commuting probe-bath interactions to suppress the buildup of quantum correlations in the bath. The resulting bath polarization is thereby exponentially enhanced. The underlying quantum thermodynamic principles have far-reaching implications for a broad range of quantum technological applications.

In this book, Henry Bar, physicist and the first quantum superhero, guides the reader through the amazing quantum world. His hair-raising adventures in his perilous struggle for quantum coherence are graphically depicted by comics and thoroughly explained to the lay reader. Behind each adventure lies a key concept in quantum physics. These concepts range from the basic quantum coherence and entanglement through tunnelling and the recently discovered quantumdecoherence control, to the principles of the emerging technologies of quantum communication and computing. The explanations of the concepts are accessible, but nonetheless rigorous and detailed. They are followed by an account of the broader context of these concepts, their historic perspective, current status and forthcoming developments. Finally, thought-provoking philosophical and cultural implications of these concepts are discussed. The mathematical appendices of all chapters cover in a straightforward manner the core aspects of quantum physics at the level of a university introductory course. The Quantum Matrix presents an entertaining, popular, yet comprehensive picture of quantum physics . It can be read as a light-hearted illustrated tale, a philosophical treatise, or a textbook. Either way, the book lets the reader delve deeply into the wondrous quantum world from diverse perspectives and obtain glimpses into the quantum technologies that are about to reshape our lives. This book offers the reader an enjoyable and rewarding voyage through the quantumworld.

Soliton solutions are studied for paraxial wave propagation with intensity-dependent dispersion. Although the corresponding Lagrangian density has a singularity, analytical solutions, derived by the pseudo-potential method and the corresponding phase diagram, exhibit one- and two-humped solitons with almost perfect agreement to numerical solutions. The results obtained in this work reveal a hitherto unexplored area of soliton physics associated with nonlinear corrections to wave dispersion. (C) 2020 Optical Society of America

Developing quantum machines which can outperform their classical counterparts, thereby achieving quantum supremacy or quantum advantage, is a major aim of the current research on quantum thermodynamics and quantum technologies. Here, we show that a fast-modulated cyclic quantum heat machine operating in the non-Markovian regime can lead to significant heat current and power boosts induced by the anti-Zeno effect. Such boosts signify a quantum advantage over almost all heat machines proposed thus far that operate in the conventional Markovian regime, where the quantumness of the system-bath interaction plays no role. The present effect owes its origin to the time-energy uncertainty relation in quantum mechanics, which may result in enhanced system-bath energy exchange for modulation periods shorter than the bath correlation-time.

### 2019

We propose to implement a quantized thermal machine based on a mixture of two atomic species. One atomic species implements the working medium and the other implements two (cold and hot) baths. We show that such a setup can be employed for the refrigeration of a large bosonic cloud starting above and ending below the condensation threshold. We analyze its operation in a regime conforming to the quantized Otto cycle and discuss the prospects for continuous-cycle operation, addressing the experimental as well as theoretical limitations. Beyond its applicative significance, this setup has a potential for the study of fundamental questions of quantum thermodynamics.

We put forward a quantum-optical model for a thermal diode based on heat transfer between two thermal baths through a pair of interacting qubits. We find that if the qubits are coupled by a Raman field that induces an anisotropic interaction, heat flow can become nonreciprocal and undergoes rectification even if the baths produce equal dissipation rates of the qubits, and these qubits can be identical, i.e., mutually resonant. The heat flow rectification is explained by four-wave mixing and Raman transitions between dressed states of the interacting qubits and is governed by a global master equation. The anisotropic two-qubit interaction is the key to the operation of this simple quantum thermal diode, whose resonant operation allows for high-efficiency rectification of large heat currents. Effects of spatial overlap of the baths are addressed. We discuss the possible realizations of the model in various platforms, including optomechanical setups, systems of trapped ions, and circuit QED.

We investigate the evolution of a target qubit caused by its multiple random collisions with N-qubit clusters. Depending on the cluster state, the evolution of the target qubit may correspond to its effective interaction with a thermal bath, a coherent (laser) drive, or a squeezed bath. In cases where the target qubit relaxes to a thermal state, its dynamics can exhibit a quantum advantage, whereby the target-qubit temperature can be scaled up proportionally to N-2 and the thermalization time can be shortened by a similar factor, provided the appropriate coherence in the cluster is prepared by nonthermal means. We dub these effects quantum superthermalization because of the analogies to superradiance. Experimental realizations of these effects are suggested.

Interesting effects arise in cyclic machines where both heat and ergotropy transfer take place between the energising bath and the system (the working fluid). Such effects correspond to unconventional decompositions of energy exchange between the bath and the system into heat and work, respectively, resulting in efficiency bounds that may surpass the Carnot efficiency. However, these effects are not directly linked with quantumness, but rather with heat and ergotropy, the likes of which can be realised without resorting to quantum mechanics.

We show that the temperature of a cavity field can be drastically varied by its interaction with suitably entangled atom pairs (dimers) traversing the cavity under realistic atomic decoherence. To this end we resort to the hitherto untapped resource of naturally entangled dimers whose state can be simply controlled via molecular dissociation, collisions forming the dimer, or unstable dimers such as positronium. Depending on the chosen state of the dimer, the cavity-field mode can be driven to a steady-state temperature that is either much lower or much higher than the ambient temperature, despite adverse effects of cavity loss and atomic decoherence. Entangled dimers enable much broader range of cavity temperature control than single "phaseonium" atoms with coherently superposed levels. Such dimers are shown to constitute highly caloric fuel that can ensure high efficiency or power in photonic thermal engines. Alternatively, they can serve as controllable thermal baths for quantum simulation of energy exchange in photosynthesis or quantum annealing.

### 2018

We study the impact of cooperative many-body effects on the operation of periodically-driven quantum thermal machines, particularly heat engines and refrigerators. In suitable geometries, N two-level atoms can exchange energy with the driving field and the (hot and cold) thermal baths at a faster rate than a single atom due to their SU(2) symmetry that causes the atoms to behave as a collective spin-N/2 particle. This cooperative effect boosts the power output of heat engines compared to the power output of N independent, incoherent, heat engines. In the refrigeration regime, similar cooling-power boost takes place.

Heat engines, which cyclically transform heat into work, are ubiquitous in technology. Lasers and masers may be viewed as heat engines that rely on population inversion or coherence in the active medium. Here we put forward an unconventional paradigm of a remarkably simple and robust electromagnetic heat-powered engine that bears basic differences to any known maser or laser: The proposed device makes use of only one Raman transition and does not rely on population inversion or coherence in its two-level working medium. Nor does it require any coherent driving. The engine can be powered by the ambient temperature difference between the sky and the ground surface. Its autonomous character and "free" power source make this engine conceptually and technologically enticing.

The purpose of this article, which is our contribution to Wolfgang Schleich's Festschrift, is to present an unconventional perspective of two fundamental, interrelated problems: the emergence of classicality and the observer's role in quantum mechanics. In our perspective, the decoherence of quantum states of a system or its measuring device (meter) by the environment cannot replace the role of the observer, nor can it provide the ultimate explanation of the transition of the system from quantumness to classicality. The reason is that decoherence, despite appearances, typically does not irretrievably obliterate the information on the system's state. Even in cases where the environment has the potential of erasing this information, the observer can negate decoherence effects in the meter or the system by dynamical control. We contend that the choice of measuring bases and observables is largely up to the controller-observer (CO) that need not possess unlimited resources in order to steer or freeze (at will) the system-state evolution and its quantumness, notwithstanding the environment effects. An analogy is drawn between the outlined approach and Lamarckism, the theory of evolution that preceded Darwinism. Quantum Lamarckism expresses our view of evolution as functional adaptation of the system to the interplay between environmental and CO effects. In our view, both conceptually and practically, decoherence may be deemed non-essential for determining the evolution of a quantum system embedded in its environment, provided the CO has an adequate, albeit limited, arsenal of resources.

According to the second law, the efficiency of cyclic heat engines is limited by the Carnot bound that is attained by engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase. Quantum engines operating between a thermal and a squeezed-thermal bath have been shown to surpass this bound. Yet, their maximum efficiency cannot be determined by the reversibility condition, which may yield an unachievable efficiency bound above unity. Here we identify the fraction of the exchanged energy between a quantum system and a bath that necessarily causes an entropy change and derive an inequality for this change. This inequality reveals an efficiency bound for quantum engines energised by a non-thermal bath. This bound does not imply reversibility, unless the two baths are thermal. It cannot be solely deduced from the laws of thermodynamics.

### 2017

We propose a hitherto-unexplored concept in quantum thermodynamics: catalysis of heat-to-work conversion by quantum nonlinear pumping of the piston mode which extracts work from the machine. This concept is analogous to chemical reaction catalysis: Small energy investment by the catalyst (pump) may yield a large increase in heat-to-work conversion. Since it is powered by thermal baths, the catalyzed machine adheres to the Carnot bound, but may strongly enhance its efficiency and power compared with its noncatalyzed counterparts. This enhancement stems from the increased ability of the squeezed piston to store work. Remarkably, the fraction of piston energy that is convertible into work may then approach unity. The present machine and its counterparts powered by squeezed baths share a common feature: Neither is a genuine heat engine. However, a squeezed pump that catalyzes heat-to-work conversion by small investment of work is much more advantageous than a squeezed bath that simply transduces part of the work invested in its squeezing into work performed by the machine.

### 2016

We present a comprehensive theory of heat engines (HE) based on a quantum-mechanical "working fluid" (WF) with periodically modulated energy levels. The theory is valid for any periodicity of driving Hamiltonians that commute with themselves at all times and do not induce coherence in the WF. Continuous and stroke cycles arise in opposite limits of this theory, which encompasses hitherto unfamiliar cycle forms, dubbed here hybrid cycles. The theory allows us to discover the speed, power, and efficiency limits attainable by incoherently operating multilevel HE depending on the cycle form and the dynamical regimes.

A universal approach to decoherence control combined with quantum estimation theory reveals a critical behavior, akin to a phase transition, of the information obtainable by a qubit probe concerning the memory time of environmental fluctuations of generalized Ornstein-Uhlenbeck processes. The criticality is intrinsic to the environmental fluctuations but emerges only when the probe is subject to suitable dynamical control aimed at inferring the memory time. A sharp transition is anticipated between two dynamical phases characterized by either a short or long memory time compared to the probing time. This phase transition of the environmental information is a fundamental feature that characterizes open quantum-system dynamics and is important for attaining the highest estimation precision of the environment memory time under experimental limitations.

Diverse models of engines energised by quantum-coherent, hence non-thermal, baths allow the engine efficiency to transgress the standard thermodynamic Carnot bound. These transgressions call for an elucidation of the underlying mechanisms. Here we show that non-thermal baths may impart not only heat, but also mechanical work to a machine. The Carnot bound is inapplicable to such a hybrid machine. Intriguingly, it may exhibit dual action, concurrently as engine and refrigerator, with up to 100% efficiency. We conclude that even though a machine powered by a quantum bath may exhibit an unconventional performance, it still abides by the traditional principles of thermodynamics.

Nonlinear optical phenomena are typically local. Here, we predict the possibility of highly nonlocal optical nonlinearities for light propagating in atomic media trapped near a nano-waveguide, where long-range interactions between the atoms can be tailored. When the atoms are in an electromagnetically induced transparency configuration, the atomic interactions are translated to long-range interactions between photons and thus to highly nonlocal optical nonlinearities. We derive and analyze the governing nonlinear propagation equation, finding a roton-like excitation spectrum for light and the emergence of order in its output intensity. These predictions open the door to studies of unexplored wave dynamics and many-body physics with highly nonlocal interactions of optical fields in one dimension. (C) 2016 Optical Society of America

In this paper, we address the question: To what extent is the quantum state preparation of multiatom clusters (before they are injected into the microwave cavity) instrumental for determining not only the kind of machine we may operate, but also the quantitative bounds of its performance? Figuratively speaking, if the multiatom cluster is the "crude oil", the question is: Which preparation of the cluster is the refining process that can deliver a "gasoline" with a "specific octane"? We classify coherences or quantum correlations among the atoms according to their ability to serve as: (i) fuel for nonthermal machines corresponding to atomic states whose coherences displace or squeeze the cavity field, as well as cause its heating; and (ii) fuel that is purely "combustible", i.e., corresponds to atomic states that only allow for heat and entropy exchange with the field and can energize a proper heat engine. We identify highly promising multiatom states for each kind of fuel and propose viable experimental schemes for their implementation.

*Advances in Chemical Physics*. Vol. 159. p. 137-218 Abstract

Coherence control was originally conceived by Shapiro and Brumer for closed quantum systems. In open quantum systems, the environment hampers or destroys coherence. Nevertheless, the Kurizki-Shapiro-Brumer coherent photocurrent control showed partial resilience to decoherence. Still, decoherence control is an essential prerequisite to our ability to fully exploit quantum coherence for any operational task. Yet decoherence control need not employ coherent fields: it may be incoherent. In operational tasks such as the preparation, transformation, transmission, and detection of quantumstates, environmental (bath) effects can be suppressed by dynamical decoupling, or by the more general incoherent dynamical control by modulation developed by our group. The resulting control dynamics must be Zeno-like in order to yield suppressed coupling to the bath in unitary operational tasks. There are however tasks which cannot be implemented by closed-system (unitary) evolution, in particular those involving a change of the system's entropy. Such tasks necessitate efficient coupling to a bath for their implementation. Examples are the use of measurements to cool (purify) a system, to equilibrate it, or harvest (and convert) energy from the environment. If the underlying dynamics is anti-Zeno like, enhancement of this coupling to the bath will occur and thereby facilitate the task, as discovered by us. A general task may also require state and energy transfer between non-interacting parties via shared modes of the bath. For such tasks, a more subtle interplay of Zeno and anti-Zeno dynamics may be optimal. We have therefore constructed a general framework for optimizing the way a system interacts with its environment to achieve a desired task. This optimization consists in adjusting a given "score" that quantifies the success of the task, such as the targeted fidelity, purity, entropy, energy or state transfer probability by dynamical modification of the system-bath coupling spectrum on demand.

We explore the ability of a qubit probe to characterize unknown parameters of its environment. By resorting to the quantum estimation theory, we analytically find the ultimate bound on the precision of estimating key parameters of a broad class of ubiquitous environmental noises ("baths") which the qubit may probe. These include the probe-bath coupling strength, the correlation time of generic types of bath spectra, and the power laws governing these spectra, as well as their dephasing times T2. Our central result is that by optimizing the dynamical control on the probe under realistic constraints one may attain the maximal accuracy bound on the estimation of these parameters by the least number of measurements possible. Applications of this protocol that combines dynamical control and estimation theory tools to quantum sensing are illustrated for a nitrogen-vacancy center in diamond used as a probe.

### 2015

In this article we argue that thermal reservoirs (baths) are potentially useful resources in processes involving atoms interacting with quantized electromagnetic fields and their applications to quantum technologies. One may try to suppress the bath effects by means of dynamical control, but such control does not always yield the desired results. We wish instead to take advantage of bath effects, that do not obliterate 'quantumness' in the system-bath compound. To this end, three possible approaches have been pursued by us. (i) Control of a quantum system faster than the correlation time of the bath to which it couples: such control allows us to reveal quasi-reversible/coherent dynamical phenomena of quantum open systems, manifest by the quantum Zeno or anti-Zeno effects (QZE or AZE, respectively). Dynamical control methods based on the QZE are aimed not only at protecting the quantumness of the system, but also diagnosing the bath spectra or transferring quantum information via noisy media. By contrast, AZE-based control is useful for fast cooling of thermalized quantum systems. (ii) Engineering the coupling of quantum systems to selected bath modes: this approach, based on field-atom coupling control in cavities, waveguides and photonic band structures, allows one to drastically enhance the strength and range of atom-atom coupling through the mediation of the selected bath modes. More dramatically, it allows us to achieve bath-induced entanglement that may appear paradoxical if one takes the conventional view that coupling to baths destroys quantumness. (iii) Engineering baths with appropriate non-flat spectra: this approach is a prerequisite for the construction of the simplest and most efficient quantum heat machines (engines and refrigerators). We may thus conclude that often thermal baths are 'more friends than foes' in quantum technologies.

We present the general theory of a quantum heat machine based on an N-level system (working medium) whose N-1 excited levels are degenerate, a prerequisite for steady-state interlevel coherence. Our goal is to find out the extent to which coherence in the working medium is an asset for heat machines. The performance bounds of such a machine are common to (reciprocating) cycles that consist of consecutive strokes and continuous cycles wherein the periodically driven system is constantly coupled to cold and hot heat baths. Intriguingly, we find that the machine's performance strongly depends on the relative orientations of the transition-dipole vectors in the system. Perfectly aligned (parallel) transition dipoles allow for steady-state coherence effects, but also give rise to dark states, which hinder steady-state thermalization and thus reduce the machine's performance. Similar thermodynamic properties hold for N two-level atoms conforming to the Dicke model. We conclude that level degeneracy, but not necessarily coherence, is a thermodynamic resource, equally enhancing the heat currents and the power output of the heat machine. By contrast, the efficiency remains unaltered by this degeneracy and adheres to the Carnot bound.

We revisit the thermodynamic bounds of work extraction in simple quantum heat machines subject to control by frequent modulations that do not comply with adiabatic assumptions. The laws of thermodynamics are obeyed, yet anomalous deviations from the known bounds are revealed.

We explore means of maximizing the power output of a heat engine based on a periodically-driven quantum system that is constantly coupled to hot and cold baths. It is shown that the maximal power output of such a heat engine whose "working fluid" is a degenerate V-type three-level system is that generated by two independent two-level systems. Hence, level degeneracy is a thermodynamic resource that may effectively double the power output. The efficiency, however, is not affected. We find that coherence is not an essential asset in such multilevel-based heat engines. The existence of two thermalization pathways sharing a common ground state suffices for power enhancement.

Nonlinear optical propagation in cholesteric liquid crystals (CLC) with a spatially periodic helical molecular structure is studied experimentally and modeled numerically. This periodic structure can be seen as a Bragg grating with a propagation stopband for circularly polarized light. The CLC nonlinearity can be strengthened by adding absorption dye, thus reducing the nonlinear intensity threshold and the necessary propagation length. As the input power increases, a blue shift of the stopband is induced by the self-defocusing nonlinearity, leading to a substantial enhancement of the transmission and spreading of the beam. With further increase of the input power, the self-defocusing nonlinearity saturates, and the beam propagates as in the linear-diffraction regime. A system of nonlinear couple-mode equations is used to describe the propagation of the beam. Numerical results agree well with the experiment findings, suggesting that modulation of intensity and spatial profile of the beam can be achieved simultaneously under low input intensities in a compact CLC-based micro-device.

An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field.

We explore, theoretically and experimentally, a method for cooling a broadband heat reservoir, via its laser-assisted collisions with two-level atoms followed by their fluorescence. This method is shown to be advantageous compared to existing laser-cooling methods in terms of its cooling efficiency, the lowest attainable temperature for broadband baths, and its versatility: it can cool down any heat reservoir, provided the laser is red detuned from the atomic resonance. It is applicable to cooling down both dense gaseous and condensed media.

*Advances In Atomic, Molecular, and Optical Physics, 2015*. Lin C. C., Arimondo E. & Yelin S. F.(eds.). p. 329-407 Abstract

In this review, the debated rapport between thermodynamics and quantum mechanics is addressed in the framework of the theory of periodically driven/controlled quantum-thermodynamic machines. The basic model studied here is that of a two-level system (TLS), whose energy is periodically modulated while the system is coupled to thermal baths. When the modulation interval is short compared to the bath memory time, the system-bath correlations are affected, thereby causing cooling or heating of the TLS, depending on the interval. In steady state, a periodically modulated TLS coupled to two distinct baths constitutes the simplest quantum heat machine (QHM) that may operate as either an engine or a refrigerator, depending on the modulation rate. We find their efficiency and power-output bounds and the conditions for attaining these bounds. An extension of this model to multilevel systems shows that the QHM power output can be boosted by the multilevel degeneracy.These results are used to scrutinize basic thermodynamic principles: (i) externally driven/modulated QHMs may attain the Carnot efficiency bound, but when the driving is done by a quantum device (piston), the efficiency strongly depends on its initial quantum state. Such dependence has been unknown thus far. (ii) The refrigeration rate effected by QHMs does not vanish as the temperature approaches absolute zero for certain quantized baths, e.g., magnons, thus challenging Nernst's unattainability principle. (iii) System-bath correlations allow more work extraction under periodic control than that expected from the Szilard-Landauer principle, provided the period is in the non-Markovian domain. Thus, dynamically controlled QHMs may benefit from hitherto unexploited thermodynamic resources.

We analyze work extraction from an autonomous (self-contained) heat-powered optomechanical setup. The initial state of the quantized mechanical oscillator plays a key role. As the initial mean amplitude of the oscillator decreases, the resulting efficiency increases. In contrast to laser-powered self-induced oscillations, work extraction from a broadband heat bath does not require coherence or phase-locking: an initial phase-averaged coherent state of the oscillator still yields work, as opposed to an initial Fock-state.

### 2014

The interaction between noncolinear laser and relativistic electron beams in a static magnetic undulator has been studied within the framework of dispersion equations. For a free-electron laser without inversion (FELWI), the threshold parameters are found. The large-amplification regime should be used to bring an FELWI above the threshold laser power.

We explore the dependence of the performance bounds of heat engines and refrigerators on the initial quantum state and the subsequent evolution of their piston, modeled by a quantized harmonic oscillator. Our goal is to provide a fully quantized treatment of self-contained (autonomous) heat machines, as opposed to their prevailing semiclassical description that consists of a quantum system alternately coupled to a hot or a cold heat bath and parametrically driven by a classical time-dependent piston or field. Here, by contrast, there is no external time-dependent driving. Instead, the evolution is caused by the stationary simultaneous interaction of two heat baths (having distinct spectra and temperatures) with a single two-level system that is in turn coupled to the quantum piston. The fully quantized treatment we put forward allows us to investigate work extraction and refrigeration by the tools of quantum-optical amplifier and dissipation theory, particularly, by the analysis of amplified or dissipated phase-plane quasiprobability distributions. Our main insight is that quantum states may be thermodynamic resources and can provide a powerful handle, or control, on the efficiency of the heat machine. In particular, a piston initialized in a coherent state can cause the engine to produce work at an efficiency above the Carnot bound in the linear amplification regime. In the refrigeration regime, the coefficient of performance can transgress the Carnot bound if the piston is initialized in a Fock state. The piston may be realized by a vibrational mode, as in nanomechanical setups, or an electromagnetic field mode, as in cavity-based scenarios.

Quantum electromagnetic fluctuations induce forces between neutral particles, known as the van der Waals and Casimir interactions. These fundamental forces, mediated by virtual photons from the vacuum, play an important role in basic physics and chemistry and in emerging technologies involving, e.g., microelectromechanical systems or quantum information processing. Here we show that these interactions can be enhanced by many orders of magnitude upon changing the character of the mediating vacuum modes. By considering two polarizable particles in the vicinity of any standard electric transmission line, along which photons can propagate in one dimension, we find a much stronger and longer-range interaction than in free space. This enhancement may have profound implications on many-particle and bulk systems and impact the quantum technologies mentioned above. The predicted giant vacuum force is estimated to be measurable in a coplanar waveguide line.

We show that atoms subject to laser radiation may form a non-additive many-body system on account of their longrange forces, when the atoms are trapped in the vicinity of a fiber with a Bragg grating. When the laser frequency is inside the grating's bandgap but very close to its edge, we find that the range and strength of the laser-induced interaction becomes substantially enhanced, due to the large density of states near the edge, while the competing process of scattering to the fiber is inhibited. The dynamics of the atomic positions in this system conforms to a prominent model of statistical physics which exhibits slow relaxation. This suggests the possibility of using laserilluminated atoms to study the characteristics of non-additive systems.

We propose a method of optimally controlling the tradeoff of speed and fidelity of state transfer through a noisy quantum channel (spin-chain). This process is treated as qubit state-transfer through a fermionic bath. We show that dynamical modulation of the boundary-qubits levels can ensure state transfer with the best tradeoff of speed and fidelity. This is achievable by dynamically optimizing the transmission spectrum of the channel. The resulting optimal control is robust against both static and fluctuating noise in the channels spin-spin couplings. It may also facilitate transfer in the presence of diagonal disorder (on site energy noise) in the channel.

Polarizable dipoles, such as atoms, molecules, or nanoparticles, subject to laser radiation may attract or repel each other. We derive a general formalism in which such laser-induced dipole-dipole interactions (LIDDIs) in any geometry and for any laser strength are described in terms of the resonant dipole-dipole interaction (RDDI) between dipoles dressed by the laser. This approach provides a simple route towards the analysis of LIDDI in a general geometry. Our general results reveal LIDDI effects due to nonlinear dipolar response to the laser, previously unaccounted for. The origin of these nonlinear effects is discussed. Our general formalism is illustrated for LIDDI between atoms in a cavity.

We review the effects of frequent, impulsive quantum nondemolition measurements of the energy of two-level systems, alias qubits, in contact with a thermal bath. The resulting entropy and temperature of the system subject to measurements at intervals below the bath memory (Markovianity) time are completely determined by the measurement rate. Namely, they are unrelated to what is expected by standard thermodynamical behavior that holds for Markovian baths. These anomalies allow for very fast control of heating, cooling, and state-purification (entropy reduction) of qubits, much sooner than their thermal equilibration time. We further show that frequent measurements may enable the extraction of work in a closed cycle from the system-bath interaction (correlation) energy, a hitherto unexploited work resource. They allow for work even if no information is gathered or the bath is at zero temperature, provided the cycle is within the bath memory time.

### 2013

We investigate heat-pumped single-mode amplifiers of quantized fields in high-Q cavities based on noninverted two-level systems. Their power generation is shown to crucially depend on the capacity of the quantum state of the field to accumulate useful work. By contrast, the energy gain of the field is shown to be insensitive to its quantum state. Analogies and differences with masers are explored.

We show that frequent nondemolition measurements of a quantum system immersed in a thermal bath allow the extraction of work in a closed cycle from the system-bath interaction (correlation) energy, a hitherto unexploited work resource. It allows for work even if no information is gathered or the bath is at zero temperature, provided the cycle is within the bath memory time. The predicted work resource may be the basis of quantum engines embedded in a bath with long memory time, such as the electromagnetic bath of a high-Q cavity coupled to two-level systems.

We consider the dispersion energy of a pair of dipoles embedded in a metallic waveguide with transverse dimension a smaller than the characteristic dipolar wavelength. We find that a sets the scale that separates retarded, Casimir-Polder-like from quasistatic, van der Waals-like interactions. Whereas in the retarded regime the energy decays exponentially with interdipolar distance, typical of evanescent waves, in the van der Waals regime, the known free-space result is obtained. This short-range scaling implies that the additivity of the dispersion interactions inside a waveguide extends to denser media, along with modifications to related Casimir effects in such structures.

We present an approach to monitoring and controlling a free quantum particle by coupling an internal (discrete) state of the particle to a detector (or probe). We consider a sequence of time-dependent, spatially localized interactions of the particle with the probe that are purely coherent (nondissipative), without mean energy-momentum exchange. We show that a sequence of such force-free interactions can freeze or deflect the particle.

We show that nonradiative interactions between atomic dipoles placed in a waveguide can give rise to deterministic entanglement at ranges much larger than their resonant wavelength. The range increases as the dipole resonance approaches the waveguide's cutoff frequency, caused by the giant density of photon modes near cutoff, a regime where the standard (perturbative) Markov approximation fails. We provide analytical theories for both the Markovian and non-Markovian regimes, supported by numerical simulations, and discuss possible experimental realizations.

A pulsed laser scenario, designed to prepare a variety of self-assembled quantum dots with nearly 100% population in a biexciton state, is proposed. We use realistic parameters for typical self-assembled quantum dots and show that two-colour sequential as well as concurrent excitation of the biexciton state can virtually eliminate unwanted exciton population and prepare a quantum dot in the biexciton state with near-deterministic accuracy. The ensuing radiative emission would be a prerequisite for a high rate, on-demand, source of entangled photons.

In traditional thermodynamics the Carnot cycle yields the ideal performance bound of heat engines and refrigerators. We propose and analyze a minimal model of a heat machine that can play a similar role in quantum regimes. The minimal model consists of a single two-level system with periodically modulated energy splitting that is permanently, weakly, coupled to two spectrally separated heat baths at different temperatures. The equation of motion allows us to compute the stationary power and heat currents in the machine consistent with the second law of thermodynamics. This dual-purpose machine can act as either an engine or a refrigerator (heat pump) depending on the modulation rate. In both modes of operation, the maximal Carnot efficiency is reached at zero power. We study the conditions for finite-time optimal performance for several variants of the model. Possible realizations of the model are discussed.

We show that a thermal reservoir can effectively act as a squeezed reservoir on atoms that are subject to energy-level modulation. For sufficiently fast and strong modulation, for which the rotating-wave approximation is broken, the resulting squeezing persists at long times. These effects are analyzed by a master equation that is valid beyond the rotating-wave approximation. As an example we consider a two-level atom in a cavity with Lorentzian linewidth, subject to sinusoidal energy modulation. A possible realization of these effects is discussed for Rydberg atoms. DOI: 10.1103/PhysRevA.87.013841

### 2012

A minimal model of a quantum refrigerator, i.e., a periodically phase-flipped two-level system permanently coupled to a finite-capacity bath (cold bath) and an infinite heat dump (hot bath), is introduced and used to investigate the cooling of the cold bath towards absolute zero (T=0). Remarkably, the temperature scaling of the cold-bath cooling rate reveals that it does not vanish as T→0 for certain realistic quantized baths, e.g., phonons in strongly disordered media (fractons) or quantized spin waves in ferromagnets (magnons). This result challenges Nernst's third-law formulation known as the unattainability principle.

We propose a method to maximize the fidelity of quantum memory implemented by a spectrally inhomogeneous spin ensemble. The method is based on preselecting the optimal spectral portion of the ensemble by judiciously designed pulses. This leads to significant improvement of the transfer and storage of quantum information encoded in the microwave or optical field.

We develop a general optimization strategy for performing a chosen unitary or nonunitary task on an open quantum system. The goal is to design a controlled time-dependent system Hamiltonian by variationally minimizing or maximizing a chosen function of the system state, which quantifies the task success (score), such as fidelity, purity, or entanglement. If the time dependence of the system Hamiltonian is fast enough to be comparable to or shorter than the response time of the bath, then the resulting non-Markovian dynamics is shown to optimize the chosen task score to second order in the coupling to the bath. This strategy can protect a desired unitary system evolution from bath-induced decoherence, but can also take advantage of the system-bath coupling so as to realize a desired nonunitary effect on the system.

We show that coupled-spin network manipulations can be made highly effective by repeated projections of the evolving quantum states onto diagonal density-matrix states (populations). As opposed to the intricately crafted pulse trains that are often used to fine-tune a complex network's evolution, the strategy hereby presented derives from the "quantum Zeno effect" and provides a highly robust route to guide the evolution by destroying all unwanted correlations (coherences). We exploit these effects by showing that a relaxationlike behavior is endowed to polarization transfers occurring within a N-spin coupled network. Experimental implementations yield coupling constant determinations for complex spin-coupling topologies, as demonstrated within the field of liquid-state nuclear magnetic resonance.

Since the pioneering works of Carr-Purcell and Meiboom-Gill [Carr HY, Purcell EM (1954) Phys Rev 94:630; Meiboom S, Gill D (1985) Rev Sci Instrum 29:688], trains of π-pulses have featured amongst the main tools of quantum control. Echo trains find widespread use in nuclear magnetic resonance spectroscopy (NMR) and imaging (MRI), thanks to their ability to free the evolution of a spin-1/2 from several sources of decoherence. Spin echoes have also been researched in dynamic decoupling scenarios, for prolonging the lifetimes of quantum states or coherences. Inspired by this search we introduce a family of spin-echo sequences, which can still detect site-specific interactions like the chemical shift. This is achieved thanks to the presence of weak environmental fluctuations of common occurrence in high-field NMR - such as homonuclear spin-spin couplings or chemical/biochemical exchanges. Both intuitive and rigorous derivations of the resulting "selective dynamical recoupling" sequences are provided. Applications of these novel experiments are given for a variety of NMR scenarios including determinations of shift effects under inhomogeneities overwhelming individual chemical identities, and model-free characterizations of chemically exchanging partners.

### 2011

We investigate quantum information processing, transfer and storage in hybrid systems comprised of diverse blocks integrated on chips. Strong coupling between superconducting (SC) qubits and ensembles of ultracold atoms or NV-center spins is mediated by a microwave transmission-line resonator that interacts near-resonantly with the atoms or spins. Such hybrid devices allow us to benefit from the advantages of each block and compensate for their disadvantages. Specifically, the SC qubits can rapidly implement quantum logic gates, but are "noisy" (prone to decoherence), while collective states of the atomic or spin ensemble are "quiet"(protected from decoherence) and thus can be employed for storage of quantum information. To improve the overall performance (fidelity) of such devices we discuss dynamical control to optimize quantum state-transfer from a "noisy" qubit to the "quiet" storage ensemble. We propose to maximize the fidelity of transfer and storage in a spectrally inhomogeneous spin ensemble, by pre-selecting the optimal spectral portion of the ensemble. Significant improvements of the overall fidelity of hybrid devices are expected under realistic conditions. Experimental progress towards the realization of these schemes is discussed.

Historically, the completeness of quantum theory has been questioned using the concept of bipartite continuous-variable entanglement. The non-classical correlations (entanglement) between the two subsystems imply that the observables of one subsystem are determined by the measurement choice on the other, regardless of the distance between the subsystems. Nowadays, continuous-variable entanglement is regarded as an essential resource, allowing for quantum enhanced measurement resolution, the realization of quantum teleportation and quantum memories, or the demonstration of the Einstein-Podolsky-Rosen paradox. These applications rely on techniques to manipulate and detect coherences of quantum fields, the quadratures. Whereas in optics coherent homodyne detection of quadratures is a standard technique, for massive particles a corresponding method was missing. Here we report the realization of an atomic analogue to homodyne detection for the measurement of matter-wave quadratures. The application of this technique to a quantum state produced by spin-changing collisions in a Bose-Einstein condensate reveals continuous-variable entanglement, as well as the twin-atom character of the state. Our results provide a rare example of continuous-variable entanglement of massive particles. The direct detection of atomic quadratures has applications not only in experimental quantum atom optics, but also for the measurement of fields in many-body systems of massive particles.

Existing optimal control methods of open quantum systems rely on extensive numerical simulations of the dynamics in the presence of a bath, or alternatively ignore the exact bath dynamics. If the bath effects are to be treated properly on both Markovian and non-Markovian timescales using numerical simulations, the number of bath modes cannot be large. This may affect the ability to simulate realistic scenarios. Even if realistic, such simulations are hard to interpret physically. An alternative approach advocated here is to resort to a perturbative analysis provided the system-bath coupling is weak. This analysis would allow for the effects of any given bath (finite or infinite, Markovian or non-Markovian) and any control at our disposal. This poses the challenge of constructing a method for the optimization of various operations requiring proper manipulation of the system, based on a general perturbative treatment to second order in the system-bath coupling. This proposed treatment yields a universal tool for optimizing the fidelity of a given operation. It involves a fidelity-control matrix: a construct that allows us to prioritize the use of available control resources so as to maximize the operation fidelity in any given bath. As an analytically solvable example of this general method, we analyse quantum state-transfer optimization, from a 'noisy' (write-in) qubit to its 'quiet' counterpart (storage qubit). Intriguing interplay is revealed between our ability to avoid bath-induced errors that profoundly depend on the bath-memory time and the limitations imposed by leakage out of the operational subspace. Counterintuitively, under no circumstances is the fastest transfer optimal (for a given transfer energy).

Decoherence is a major obstacle to any practical implementation of quantum information processing. One of the leading strategies to reduce decoherence is dynamical decoupling-the use of an external field to average out the effect of the environment. The decoherence rate under any control field can be calculated if the spectrum of the coupling to the environment is known. We present a direct measurement of the bath-coupling spectrum in an ensemble of optically trapped ultra-cold atoms, by applying a spectrally narrow-band control field. The measured spectrum follows a Lorentzian shape at low frequencies but exhibits non-monotonic features at higher frequencies due to the oscillatory motion of the atoms in the trap. These features agree with our analytical models and numerical Monte Carlo simulations of the collisional bath. From the inferred bath-coupling spectrum, we predict the performance of some well-known dynamical decoupling sequences. We then apply these sequences in experiment and compare the results to predictions, finding good agreement in the weak-coupling limit. Thus, our work establishes experimentally the validity of the overlap integral formalism and is an important step towards the implementation of an optimal dynamical decoupling sequence for a given measured bath spectrum.

As a rule, the coupling of a quantum system to an uncontrollable thermal reservoir (a "bath") gives rise to the system's decoherence, i.e., the destruction of its unitary coherent evolution [1]. Not less common is the rule that the more complex the quantum system, the more detrimental are the bath effects [2]. Here we point out that the coupling of a complex quantum system to a bath may actually induce advantageous coherent dynamics. Namely, an exact solution for a quantum many-body system characterized by large angular momentum (or spin) that is coupled to a thermal bath reveals a hitherto unexplored general effect: bath-induced effectively nonlinear evolution. This evolution can drive the large-spin system into a macroscopic quantum-superposition ("Schroedinger-cat") state [3, 4]. Such counter-intuitive bath-induced effects should be observable in various setups on long (Markovian) time scales. They change our perspective of non-classicality in open many-body quantum systems. Namely, the bath may cause rather than impede the formation of distinctly non-classical Schroedinger-cat states, despite their fragility in the presence of a bath [2, 5].

We show, using an exactly solvable model, that nonlinear dynamics is induced in a double-well Bose-Einstein condensate (BEC) by collisions with a thermal reservoir. This dynamics can facilitate the creation of phase or number squeezing and, at longer times, the creation of macroscopic nonclassical superposition states. Enhancement of these effects is possible by loading the reservoir atoms into an optical lattice.

Hollow-core photonic-crystal waveguides filled with cold atoms can support giant optical nonlinearities through nondispersive propagation of light tightly confined in the transverse direction. Here we explore electromagnetically induced transparency is such structures, considering a pair of counterpropagating weak quantum fields in the medium of coherently driven atoms in the ladder configuration. Strong dipole-dipole interactions between optically excited, polarized Rydberg states of the atoms translate into a large dispersive interaction between the two fields. This can be used to attain a spatially homogeneous conditional phase shift of π for two single-photon pulses, realizing a deterministic photonic phase gate, or to implement a quantum nondemolition measurement of the photon number in the signal pulse by a coherent probe, thereby achieving a heralded source of single- or few-photon pulses.

We demonstrate that collective continuous variables of two species of trapped ultracold bosonic gases can be Einstein-Podolsky-Rosen-correlated (entangled) via inherent interactions between the species. We propose two different schemes for creating these correlations-a dynamical scheme and a static scheme analogous to two-mode squeezing in quantum optics. We quantify the correlations by using known measures of entanglement and study the effect of finite temperature on these quantum correlations.

We investigate the scaling of decoherence rates and their dynamical suppression with the number N of qubits in various entangled states. Remarkably, for sufficiently large N, coherence time is always in the Zeno regime. This changes the scaling to the square root of the Markov-regime scaling. We find that a simple and effective control strategy is to locally modulate the individual qubits and thereby not only suppress the decoherence rate of each qubit, but also reduce the decoherence scaling of entangled states that are particularly fragile, from N2 to N, resulting in a dramatic reduction of the decoherence (by orders of magnitude). Surprisingly, the conditions for the effectiveness of such decoherence control are independent of N.

We demonstrate through exact solutions that a spin bath leads to stronger (faster) dephasing of a qubit than a bosonic bath with an identical bath-coupling spectrum. This difference is due to the spin-bath "dressing" by the coupling. Consequently, the quantum statistics of the bath strongly affects the pulse sequences required to dynamically decouple the qubit from its bath.

We demonstrate through an exactly solvable model that collective coupling to any thermal bath induces effectively nonlinear couplings in a quantum many-body (multispin) system. The resulting evolution can drive an uncorrelated large-spin system with high probability into a macroscopic quantum-superposition state. We discuss possible experimental realizations.

Optical microscopy with spatial resolution below the diffraction limit is at present attracting extensive attentions. Further advancement of the near-field scanning optical microscopy (NSOM), a practical super-resolution microscopy, is mainly limited by the low transmission of optical power through the nano-meter apex. This work shows that lightwave can be efficiently delivered to a sub-100 nm apex inside a tapered metallic guiding structure. The enhanced light delivery, about 5-fold, is made possible with an adaptive optimization of the transmission via a spatial light phase-modulator. Numerical simulation shows the mechanism for the efficient light delivery to be the selective excitation of predominantly the lowest-order transverse component of standing wavevector with proper input wavefront modulation, hence favoring the transmission of lightwave in the longitudinal direction. The demonstration of such efficient focusing, to about full-width at half-maximum of a quarter wavelength, has a direct and immediate application in the improvement of the existing NSOMs.

### 2010

We introduce a model of a two-dimensional (2D) self-attractive medium embedded into a quasi-1D symmetric double-well potential (DWP), whose depth is subject to periodic modulations (management). The model applies to matter waves in Bose-Einstein condensates (BECs), as well as to the nonlinear transmission of light (in spatial and temporal domains alike). It is known that, in the absence of the management, the DWP induces the spontaneous symmetry breaking (SSB) of 2D solitons, when their norm exceeds a critical value. Above the SSB point, symmetric solitons are unstable, while the system supports stable asymmetric ones. The DWP also admits Josephson oscillations of solitons between the two wells. We study effects of periodic modulations of the DWP's depth on the stability of symmetric, asymmetric, and oscillating solitons. Stability areas for the solitons of these three types are produced in the plane of the modulation frequency and amplitude. The shape of the stability borders is strongly affected by the proximity of the modulation frequency to the frequency of free oscillations of the soliton in the static DWP structure, the solitons being destroyed by the modulations with an arbitrarily small amplitude at the point of the exact resonance. Similar results are obtained for an extended 2D model, which combines the transverse DWP and a longitudinal periodic potential (optical lattice, in terms of BEC). The findings are compared with those reported in other recently studied management models for 1D and 2D solitons, which makes it possible to draw general conclusions about the stability limits of solitons under the resonant management.

We experimentally and theoretically demonstrate the purity (polarization) control of qubits entangled with multiple spins, using induced dephasing in nuclear magnetic resonance setups to simulate repeated quantum measurements. We show that one may steer the qubit ensemble towards a quasiequilibrium state of a certain purity by choosing suitable time intervals between dephasing operations. These results demonstrate that repeated dephasing at intervals associated with the anti-Zeno regime leads to ensemble purification, whereas those associated with the Zeno regime lead to ensemble mixing.

We propose a control mechanism for the stabilization of symmetry-broken modes in Bose-Einstein condensates and optical beams trapped in double-well potentials in the presence of symmetric or asymmetric noise. The control, based on periodic π shifts of the phase in one well, is demonstrated for solitons and in the two-mode approximation. The latter setting is considered in both the mean-field and quantum (Bose-Hubbard) regimes.

We consider an unexplored regime of open quantum systems that relax via coupling to a bath while being monitored by an energy meter. We show that any such system inevitably reaches an equilibrium (quasi-steady) state controllable by the effective rate of monitoring. In the non-Markovian regime, this approach suggests the possible 'freezing' of states, by choosing monitoring rates that set a non-thermal equilibrium state to be the desired one. For measurement rates high enough to cause the quantum Zeno effect, the only steady state is the fully mixed state, due to the breakdown of the rotating wave approximation. Regardless of the monitoring rate, all the quasi-steady states of an observed open quantum system live only as long as the Born approximation holds, namely the bath entropy does not change. Otherwise, both the system and the bath converge to their fully mixed states.

We study deviations from thermal equilibrium between two-level systems (TLS) and a bath by frequent and brief quantum measurements of the TLS energy-states. The resulting entropy and temperature of both the system and the bath are found to be completely determined by the measurement rate, and unrelated to what is expected by standard thermodynamical rules that hold for Markovian baths. These anomalies allow for very fast control heating, cooling and state-purification (entropy reduction) of quantum systems much sooner than their thermal equilibration time.

We propose a technique that allows to simultaneously perform universal control of the evolution operator of a system and compensate for the first-order contribution of any Hermitian constant noise and the action of the environment. We show that, at least, a three-valued Hamiltonian is needed in order to protect the system against any such noise and propose an explicit algorithm for finding an appropriate control sequence. This algorithm is applied to numerically design a safe gate in an atomic qutrit.

We put forward a general strategy for dynamic control that ensures bath-optimized fidelity of a desired multidimensional quantum operation in the presence of non-Markovian baths and noises with stationary autocorrelations. It benefits from the vast freedom of arbitrary, not just pulsed, time-dependent control. This allows the dramatic reduction of the invested energy and the corresponding error compared to pulsed control.

A threshold condition for amplification without inversion in a free-electron laser without inversion (FELWI) is determined. This condition is found to be too severe for the effect to be observed in an earlier suggested scheme because a threshold intensity of the field to be amplified appears to be too high. This indicates that alternative schemes have to be found for making the creation of an FELWI realistic.

We explore the effects of frequent, impulsive quantum non-demolition measurements of the energy of two-level systems (TLS), alias qubits, in contact with a thermal bath. The resulting entropy and temperature of both the system and the bath are found to be completely determined by the measurement rate, and unrelated to what is expected by standard thermodynamical rules that hold for Markovian baths. These anomalies allow for very fast control of heating, cooling and state-purification (entropy reduction) of qubits, much sooner than their thermal equilibration time.

### 2009

Dispersion and dissipation are inherent to electromagnetic wave propagation in metamaterials. We show that these inherent limitations can be overcome by a self-induced transparency pulse that stably propagates through a metamaterial sparsely doped with resonantly absorbing dopants. This pulse has the form of a hitherto unexplored backward soliton. We discuss the observable signature of this soliton.

Quantum two-state systems, known as quantum bits (qubits), are unavoidably in contact with their uncontrolled thermal environment, also known as a macroscopic 'bath'. The higher the temperature of the qubits, the more impure their quantum state and the less useful they are for coherent control or quantum logic operations, hence the desirability of cooling down the qubits as much and as fast as possible, so as to purify their state prior to the desired operation. Yet, the limit on the speed of existing cooling schemes, which are all based on Markovian principles, is either the duration of the qubit equilibration with its bath or the decay time of an auxiliary state to one of the qubit states. Here we pose the conceptual question: can one bypass this existing Markovian limit? We show that highly frequent phase shifts or measurements of the state of thermalized qubits can lead to their ultrafast cooling, within the non-Markov time domain, well before they re-equilibrate with the bath and without resorting to auxiliary states. Alternatively, such operations may lead to the cooling down of the qubit to arbitrarily low temperatures at longer times. These anomalous nonMarkov cooling processes stem from the hitherto unfamiliar coherent quantum dynamics of the qubit-bath interaction well within the bath memory time.

Initialization of quantum logic operations makes it imperative to cool down the information-carrying qubits as much and as fast as possible, so as to purify their state, or at least their ensemble average. Yet, the limit on the speed of existing cooling schemes is either the duration of the qubit equilibration with its bath or the decay time of an auxiliary state to one of the qubit states. Here we show that highly-frequent phase-shifts or measurements of the state of thermalized qubits can be designed to affect the qubit-bath entanglement so that the qubits undergo cooling, well before they re-equilibrate with the bath and without resorting to auxiliary states. These processes can be used in principally novel, advantageous, cooling schemes to assist quantum logic operations.

A general quantum noisy channel is analyzed, wherein the transmitted qubits may experience symmetry-breaking decoherence, along with memory effects. We examine generalized Bell-basis and find that the optimal basis is not the fully entangled one, but a combination of factorized and partially-entangled states in the presence of memory, asymmetry and the state-bias of the noise. Capacity-maximization is shown to be achievable by combining temporal shaping of the transmitted qubits and optimal basis selection.

We present an approach to dynamic decoherence control of finite-temperature Bose-Einstein condensates in a double-well potential. Due to the many-body interactions the standard "echo" control method becomes less effective. The approach described here takes advantage of the interaction-induced change of the spectrum, to obtain the optimal rate of π flips of the relative phase between maximally distinguishable collective states. This method is particularly useful for probing and diagnosing the decoherence dynamics.

An analytical expression is received for the effective interaction potential of a fast charged particle with the ionic crystal CsCl near the direction of axis 100 as a function of the temperature of the medium. By numerical analysis it is shown that the effective potential of axial channeling of positrons along the axis 100 of negatively charged Cl^{-} ions practically doesn't depend on temperature of the media. The wavefunction and the energy spectrum of the localized state are investigated, and the possibility is proved for the formation of metastable, two-dimensional relativistic positron systems or the positron atoms (PA), i.e. the bound state of a positron in the present case with a negatively charged axis of ions. The problem of one-photon decay of PA is investigated. The possibilities of stimulation of resonant transitions between quantum states of PA by the external hypersound are investigated in detail.

We study the effect of decoherence on dynamical phase diffusion in the two-site Bose-Hubbard model. Starting with an odd parity excited coherent state, the initial loss of single-particle coherence varies from small bound oscillations in the Rabi regime, through hyperbolic depletion in the Josephson regime, to a Gaussian decay in the Fock regime. The inclusion of local-site noise, measuring the relative number difference between the modes, is shown to enhance phase diffusion. In comparison, site-indiscriminate noise measuring the population imbalance between the two quasimomentum modes slows down the loss of single-particle coherence. Decoherence thus either enhances or suppresses phase diffusion, depending on the details of system-bath coupling and the overlap of decoherence pointer states with collisional-entanglement pointer states. The deceleration of phase diffusion due to the coupling with the environment may be viewed as a many-body quantum Zeno effect. The extended effective decay times in the presence of projective measurement are further enhanced with increasing number of particles N by a bosonic factor of N in the Fock regime and N/logN in the Josephson regime.

We examine the possibility of coherent reversible information transfer between solid-state superconducting qubits and ensembles of ultracold atoms. Strong coupling between these systems is mediated by a microwave transmission line resonator that interacts near resonantly with the atoms via their optically excited Rydberg states. The solid-state qubits can then be used to implement rapid quantum logic gates, while collective metastable states of the atoms can be employed for long-term storage and optical readout of quantum information.

We study, both experimentally and theoretically, short-time modifications of the decay of excitations in a Bose-Einstein Condensate (BEC) embedded in an optical lattice. Strong enhancement of the decay is observed compared to the Golden Rule results. This enhancement of decay increases with the lattice depth. It indicates that the description of decay modifications of few-body quantum systems also holds for decay of many-body excitations of a BEC.

Given a multilevel system coupled to a bath, we use a Feshbach P, Q partitioning technique to derive an exact trace-nonpreserving master equation for a subspace Si of the system. The resultant equation properly treats the leakage effect from Si into the remainder of the system space. Focusing on a second-order approximation, we show that a one-dimensional master equation is sufficient to study problems of quantum state storage and is a good approximation, or exact, for several analytical models. It allows a natural definition of a leakage function and its control and provides a general approach to study and control decoherence and leakage. Numerical calculations on an harmonic oscillator coupled to a room temperature harmonic bath show that the leakage can be suppressed by the pulse control technique without requiring ideal pulses.

*Atomic, Molecular And Optical Physics: New Research*. p. 491-522 Abstract

A unified theory is given of dynamically modified decay and decoherence of field-driven multipartite systems. When this universal framework is applied to two-level systems (TLS) or qubits experiencing either amplitude or phase noise (AN or PN) due to their coupling to a thermal bath, it results in completely analogous formulae for the modified decoherence rates in both cases. The spectral representation of the modified decoherence rates underscores the main insight of this approach, namely, the decoherence rate is the spectral overlap of the noise and modulation spectra. This allows us to come up with general recipes for modulation schemes for the optimal reduction of decoherence under realistic constraints. An extension of the treatment to multilevel and multipartite systems exploits intra-system symmetries to dynamically protect multipartite entangled states. Another corollary of this treatment is that entanglement, which is very susceptible to noise and can die, i.e., vanish at finite times, can be resuscitated by appropriate modulations prescribed by our universal formalism. This dynamical decoherence control is also shown to be advantageous in quantum computation setups, where control fields are applied concurrently with the gate operations to increase the gate fidelity.

We examine two set-ups that reveal different operational implications of path-phase complementarity for single photons in a Mach-Zehnder interferometer (MZI). In both set-ups, the which-way (WW) information is recorded in the polarization state of the photon serving as a 'flying which-way detector'. In the 'predictive' variant, using a fixed initial state, one obtains duality relation between the probability to correctly predict the outcome of either a which-way (WW) or which-phase (WP) measurement (equivalent to the conventional path-distinguishability-visibility). In this set-up, only one or the other (WW or WP) prediction has operational meaning in a single experiment. In the second, 'retrodictive' protocol, the initial state is secretly selected for each photon by one party, Alice, among a set of initial states which may differ in the amplitudes and phases of the photon in each arm of the MZI. The goal of the other party, Bob, is to retrodict the initial state by measurements on the photon. Here, a similar duality relation between WP and WW probabilities governs their simultaneous guesses in each experimental run.

We consider single photons propagating along two paths, with the polarization correlated to the path. Two information related aspects of this translational-internal entanglement (TIE) are analyzed: a) Using the polarization to record the path (a "flying detector" scheme), we characterize the tradeoff between path- and phase-information. b) We investigate the effects of non-Markovian noise on the two-qubit quantum channel consisting of the photon path and polarization (that are both used to encode information), and suggest noise protection schemes.

We study disturbances of thermal equilibrium between two-level systems (TLS) and a bath by frequent and brief quantum measurements of the TLS energy-states. If the measurements induce either the Zeno or the anti-Zeno regime, namely, the slowdown or speedup of the TLS relaxation, then the resulting entropy and temperature of both the system and the bath are found to be completely determined by the measurement rate, and unrelated to what is expected by standard thermodynamical rules that hold for markovian baths. These anomalies allow for very fast control heating, cooling and state-purification (entropy reduction) of quantum systems much sooner than their thermal equilibration time.

### 2008

We present the principles of universal dynamical control of open quantum systems aimed at optimally suppressing their decoherence. Several basic scenarios of this control are discussed. Our results indicate that very limited knowledge regarding the system-environment correlation is sufficient to implement control that would suppress decoherence and bring out quantum behavior in complex macroscopic systems that are embedded in thermal noisy environments.

We propose a novel protocol for the creation of macroscopic quantum superposition (MQS) states based on a measurement of a non-monotonous function of a quantum collective variable. The main advantage of this protocol is that it does not require switching on and off nonlinear interactions in the system. We predict this protocol to allow the creation of multiatom MQS by measuring the number of atoms coherently outcoupled from a two-component (spinor) Bose-Einstein condensate.

A one-step introduction of functional defects into a photonic crystal is demonstrated. By using a multi-beam phase-controlled holographic lithography, line-defects in a Bragg structure and embedded waveguides in a two-dimensional photonic crystal are fabricated. Intrinsic defect introduction into a 3-dimensional photonic crystal is also proposed. This technique gives rise to a substantial reduction of the fabrication complexity and a significant improvement on the accuracy of the functional defects in photonic crystals.

Self-pulsed lasing in the form of a coherent solitary wave train from a periodically amplifying Bragg structure is proposed. It is shown both analytically and numerically that the generated pulse train propagates in the periodically amplifying Bragg structure chip with superluminal group velocity. Its stability and coherence are in contrast with the inherent instability and chaoticity of self-pulsing from a uniform gain medium embedded in a Bragg reflector. Bragg-periodic semiconductor quantum-well heterostructures are candidates for realizing the required periodically amplifying Bragg structure.

We present a theory of dynamical control by modulation for optimal decoherence reduction. The theory is based on the non-Markovian Euler-Lagrange equation for the energy-constrained field that minimizes the average dephasing rate of a qubit for any given dephasing spectrum.

We study the effect of noise-induced dephasing on collisional phase diffusion in the two-site Bose-Hubbard model. Dephasing of the quasimomentum modes may slow down phase diffusion in the quantum Zeno limit. Remarkably, the degree of suppression is enhanced by a bosonic factor of order N/logN as the particle number N increases.

We study the two mechanisms of the interplay of long- and short-range interactions in different geometries of ultracold fermionic atomic or molecular gases. We show that in the range of validity of the one-dimensional (1D) approximation, both mechanisms yield similar superconductivity. We show that electromagnetically induced isotropic dipole-dipole interactions in a spin-polarized non-degenerate fermionic gas can cause an extremely exothermic phase transition, analogous to the isothermal collapse in gravitationally interacting star clusters. This collapse may result in fragmentation of the gas into a hot 'halo' and a highly degenerate 'core'. Possible realization is envisaged in microwave-illuminated fermionic molecular gases at microkelvin temperatures.

Heat flow between a large thermal 'bath' and a smaller system brings them progressively closer to thermal equilibrium while increasing their entropy. Fluctuations involving a small fraction of a statistical ensemble of systems interacting with the bath result in deviations from this trend. In this respect, quantum and classical thermodynamics are in agreement. Here we predict a different trend in a purely quantum mechanical setting: disturbances of thermal equilibrium between two-level systems (TLSs) and a bath, caused by frequent, brief quantum non-demolition measurements of the TLS energy states. By making the measurements increasingly frequent, we encounter first the anti-Zeno regime and then the Zeno regime (namely where the TLSs' relaxation respectively speeds up and slows down). The corresponding entropy and temperature of both the system and the bath are then found to either decrease or increase depending only on the rate of observation, contrary to the standard thermodynamical rules that hold for memory-less (Markov) baths. From a practical viewpoint, these anomalies may offer the possibility of very fast control of heat and entropy in quantum systems, allowing cooling and state purification over an interval much shorter than the time needed for thermal equilibration or for a feedback control loop.

We show that by dynamically modulating the gate fields so as to minimize the spectral overlap of the decoherence and modulation spectra specifically for each qubit, and concurrently controlling all qubits, one can significantly increase the fidelity of quantum computation. Notably, crossdecoherence, introduced by two-qubit entanglement, can be eliminated by appropriate dynamical control. In this scheme, contrary to traditional schemes, one can increase the gate duration, while, simultaneously, increasing the total gate fidelity. Experimental scenarios involving laser-driven cold-ions and coldatoms are shown to benefit from this counterintuitive scheme.

A polarized photon with well-defined orbital angular momentum that emerges from a Mach - Zehnder interferometer (MZI) is shown to seemingly circumvent wave-particle duality constraints. For certain phase differences between the MZI arms, this pattern yields both reliable which-path information and high phase sensitivity. (c) 2007 Optical Society of America.

### 2007

Dephasing is a ubiquitous phenomenon that leads to the loss of coherence in quantum systems and the corruption of quantum information. We present a universal dynamical control approach to combat dephasing during all stages of quantum computation, namely, storage and single- and two-qubit operators. We show that (a) tailoring multifrequency gate pulses to the dephasing dynamics can increase fidelity; (b) cross-dephasing, introduced by entanglement, can be eliminated by appropriate control fields; (c) counterintuitively and contrary to previous schemes, one can increase the gate duration, while simultaneously increasing the total gate fidelity.

We present and compare stochastic open-loop techniques aimed at controlling quantum coherence in dissipative environments. One approach describes the evolution time as a random non-Gaussian variable. The other implements dynamical control on non-Markovian time-scales via stochastic modulation of the system-bath coupling.

The evolution of nonlinear light fields traveling inside a resonantly absorbing Bragg reflector is studied by use of Maxwell-Bloch equations. Numerical results show that a pulse initially resembling a light bullet may effectively experience negative refraction and anomalous dispersion in the resonantly absorbing Bragg reflector.

In this paper, we develop, step by step, the framework for universal dynamical control of two-level systems (TLS) or qubits experiencing amplitude or phase noise (AN or PN) due to coupling to a thermal bath. A comprehensive arsenal of modulation schemes is introduced and applied to either AN or PN, resulting in completely analogous formulae for the decoherence rates, thus underscoring the unified nature of this universal formalism. We then address the extension of this formalism to multipartite decoherence control, where symmetries are exploited to overcome decoherence.

The aim of this paper is to revisit the implications of complementarity when we inject into a Mach Zehnder interferometer particles with internal structure, prepared in special translational-internal entangled (TIE) intraparticle states. This correlation causes the path distinguishability to be interferometric phasedependent in contrast to the standard case, where distinguishability depends on some external parameters (not interferometric phase). We show that such a TIE state permits us to detect small phase shifts along with almost perfect path distinguishability, beyond the constraints imposed by complementarity on simultaneous which-way and which-phase measurements for cases when distinguishability is uncoupled to interferometric phase.

We propose a new mechanism for tuning an atomic s-wave scattering length. The effect is caused by virtual transitions between different Zeeman sublevels via magnetic dipole-dipole interactions. These transitions give rise to an effective potential, which, in contrast to standard magnetic interactions, has an isotropic component and thus affects s-wave collisions.

We investigate conditions under which multiatom absorption of a single photon leads to cooperative decay. Our analysis reveals the symmetry properties of the multiatom Dicke states underlying the cooperative decay dynamics and their spatio-temporal manifestations, particularly, the forward-directed spontaneous emission investigated by Scully et al (2006 Phys. Rev. Lett. 96 010501).

Using quantum channels to transmit classical information has been proven to be advantageous in several scenarios. These channels have been assumed to be memoryless, meaning that consecutive transmissions of information are uncorrelated. However, as shown experimentally, such correlations do exist, and thereby retain memory of previous information. This memory complicates the protection of entangled-information transmission from decoherence. We have recently addressed these fundamental questions by developing a generalized master equation for multipartite entangled systems coupled to finite-temperature baths and subject to arbitrary external perturbations whose role is to provide dynamical protection from decay and decoherence. Here we explore and extend the foregoing strategy to quantum optical communication schemes wherein polarization-entangled photons traverse a bit-flip channel with temporal and spatial memory, such that the two channels experience cross-decoherence. We introduce a novel approach to the protection of the entangled information from decoherence in such schemes. It is based on selectively modulating the photon polarizations in each channel. We show that by applying selective modulation, one can independently control the symmetry and spatial memory attributes of the. channel. We then explore the effects of these attributes on the channel capacity. Remarkably, we show that there is a nontrivial interplay between the effects of asymmetry and memory on the channel capacity.

### 2006

We show that if internal and momentum states of an interfering particle are entangled, then by measuring its internal state we may infer both path (corpuscular) and phase (wavelike) information with practically any precision, without the complementarity constraints of which-path detection. This holds also for multipath-multistate configurations, allowing large amounts of information to be stored in a single particle. We further show that highly complex particles (e.g., molecules or macroscopic bodies) subject to fields that couple (entangle) their internal and translational (momentum) states may undergo an irresversible randomization (diffusion), manifest by the disappearance of the interference pattern, as if they are subject to decoherence. Thus, translational-internal entanglement can give rise to anomalies in quantum wavepacket propagation.

We theoretically investigate the free dispersion, scattering and disintegration of an N-particle quantum soliton by Bragg light pulses, comparing the exact quantum result with its quasiclassical (mean-field) limit. Remarkably, we find that the correlation properties of a quantum soliton approach the (mean-field) limit very rapidly as the particle number N grows. A modest discrepancy between the classical and quantum results is observed for N = 3.

An entangled multipartite system coupled to a zero-temperature bath undergoes rapid disentanglement in many realistic scenarios due to local, symmetry-breaking differences in the particle-bath couplings. We show that locally controlled perturbations, addressing each particle individually, can impose a symmetry allowing the existence of decoherence-free multipartite entangled systems.

We explore the feasibility of creating a translationally entangled state for massive particles, and its use for matter wave teleportation by means of cold-molecule Raman dissociation and association in optical traps.

A unified theory is given of dynamically modified decay and decoherence of field-driven multilevel multipartite entangled states that are weakly coupled to zero-temperature baths or undergo random phase fluctuations. The theory allows for arbitrary local differences in their coupling to the environment. Due to such differences, the optimal driving-field modulation to ensure maximal fidelity is found to substantially differ from conventional "Bang-Bang" or π-phase flips of the single-qubit evolution.

The behavior of translationally-internally entangled (TIE) states in an interferometer of the Mach-Zehnder type is studied, by means of a game whose results show that TIE states allow near-certain guessing of both path (corpuscular) and phase (wavelike) features, as opposed to conventional states that are constrained by standard complementarity.

Here we aim at setting the principles of and quantifying translational entanglement by collisions and half-collisions. In collisions, the resonance width s and the initial phase-space distributions axe shown to determine the degree of post-collisional momentum entanglement. Half-collisions (dissociation) axe shown to yield different types of approximate EPR states. We analyse a feasible realization of translational EPR entanglement and teleportation via cold-molecule Raman dissociation and subsequent collisions, resolving both practical and conceptual difficulties it has faced so far.

We present an electrostatic mechanism that gives rise to dramatic enhancements of tunneling through the inter-nuclear Coulomb-barrier. The enhancement is due to an increase in the effective negative electric charge in the mid region between two protons (deutrons) belonging to an H2+ (D2+) molecule placed inside a molecular cage, such as a fullerene molecule. This charge increase results in a marked reduction of the outer regions of the Coulomb-barrier, thereby dramatically increasing the nuclear tunneling rates. Coupled with compression of the molecular cage this effect may lead to meaningful enhancements in fusion rates.

A unified theory is given of dynamically modified decay and decoherence of field-driven multilevel multipartite entangled states that are weakly coupled to zero-temperature baths. The theory allows for arbitrary local differences in their coupling to the environment. Due to such differences, the optimal driving-field modulation to ensure maximal fidelity is found to substantially differ from conventional pi-phase flips of the single-qubit evolution.

The collective and single-electron amplification regimes of a noncollinear free-electron laser (FEL) are studied within the framework of dispersion equations. In the limit of small-signal gain the growth rates and the conditions for self-amplified excitations are found for the collective (Raman) and single-electron (Thompson) regimes. The Raman regime is shown to be preferable for the coherent spontaneous second harmonic generation by ultrarelativistic electron beams. Raman excitations in a noncollinear FEL, e.g., in an FEL without inversion, are favored by the noncollinear geometry of the electron and the laser beams, and by the relativity of the beam electrons.

We show that atoms or molecules subject to fields that couple their internal and translational (momentum) states may undergo a crossover from randomization (diffusion) to strong localization (sharpening) of their momentum distribution. The predicted crossover should be manifest by a drastic change of the interference pattern as a function of the coupling fields.

A scalable, high-performance quantum processor can be implemented using near-resonant dipole-dipole interacting dopants in a transparent solid state host. In this scheme, the qubits are represented by ground and subradiant states of effective dimers formed by pairs of closely spaced two-level systems, while the two-qubit entanglement either relies on the coherent excitation exchange between the dimers or is mediated by external laser fields.

### 2005

We show that the giant Kerr nonlinearity in the regime of electromagnetically induced transparency in vapor can give rise to the formation of Thirring-type spatial solitons, which are supported solely by cross-phase modulation that couples the two copropagating light beams.

We show that very large nonlocal nonlinear interactions between pairs of colliding slow-light pulses can be realized in atomic vapors in the regime of electromagnetically induced transparency. These nonlinearities are mediated by strong, long-range dipole-dipole interactions between Rydberg states of the multilevel atoms in a ladder configuration. In contrast to previously studied schemes, this mechanism can yield a homogeneous conditional phase shift of pi even for weakly focused single-photon pulses, thereby allowing a deterministic realization of the photonic phase gate.

To date, the translationally-entangled state originally proposed by Einstein, Podolsky and Rosen (EPR) in 1935 has not been experimentally realized for massive particles. Opatrný and Kurizki [Phys. Rev. Lett. 86, 3180 (2000)] have suggested the creation of a position- and momentum-correlated, i.e., translationally-entangled, pair of particles approximating the EPR state by dissociation of cold diatomic molecules, and further manipulation of the EPR pair effecting matter-wave teleportation. Here we aim at setting the principles of and quantifying translational entanglement by collisions and half-collisions. In collisions, the resonance width s and the initial phase-space distributions are shown to determine the degree of post-collisional momentum entanglement. Half-collisions (dissociation) are shown to yield different types of approximate EPR states. We analyse a feasible realization of translational EPR entanglement and teleportation via cold-molecule Raman dissociation and subsequent collisions, resolving both practical and conceptual difficulties it has faced so far: How to avoid entanglement loss due to the wavepacket spreading of the dissociation fragments? How to measure both position and momentum correlations of the dissociation fragments with sufficient accuracy to verify their EPR correlations? How to reliably perform two-particle (Bell) position and momentum measurements on one of the fragments and the wavepacket to be teleported?

We show that the multidimensional Zeno effect combined with non-holonomic control allows one to efficiently protect quantum systems from decoherence by a method similar to classical random coding. The method is applicable to arbitrary error-inducing Hamiltonians and general quantum systems. The quantum encoding approaches the Hamming upper bound for large dimension increases. Applicability of the method is demonstrated with a seven-qubit toy computer.

A unified theory is presented of dynamically modified decay and decoherence in driven multilevel quantum systems that are weakly coupled to arbitrary zero-temperature reservoirs. Examples of different phase and amplitude modulations are given for two-level systems (qubits). Analysis of modulations on multilevel systems is detailed with a numerical example using quasiperiodic impulsive phase jumps. The merits and disadvantages of the different modulation types are discussed.

A unified theory is given of dynamically modified decay and decoherence in driven two-level and multilevel quantum systems that are weakly coupled to arbitrary finitetemperature reservoirs and undergo random phase fluctuations. Criteria for the optimization of decoherence suppression and the limitations of this approach are obtained. For a driven qubit that is strongly coupled to the continuum edge of reservoir's spectrum, we demonstrate that only an appropriately ordered sequence of abrupt changes of the resonance frequency, near the continuum edge, can effectively protect the qubit state from decoherence.

Nonresonant light scattering off atomic Bose-Einstein condensates is predicted to give rise to hitherto unexplored composite quasiparticles: unstable polarons, i.e., local "impurities" dressed by virtual phonons. Optical monitoring of their spontaneous decay can display either Zeno or anti-Zeno deviations from the golden rule, and thereby probe the temporal correlations of elementary excitations in the condensates.

The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error correction (ancilla adding, coding and decoding) and the quantum Zeno effect. A demonstration of our method on a simple atomic system-namely, a rubidium isotope-is proposed.

We study collisions mediated by finite-range potentials as a tool for generating translational entanglement between unbound particles or multipartite systems. The general analysis is applied to one-dimensional scattering, where resonances and the initial phase-space distribution are shown to determine the degree of postcollisional entanglement.

We propose a method for controlling the decay and decoherence of a driven qubit that is strongly coupled to a reservoir, when the qubit resonance frequency is close to a continuum edge of the reservoir spectrum. This strong-coupling regime is outside the scope of existing methods of decay or decoherence control. We demonstrate that an appropriate sequence of nearly abrupt changes of the resonance frequency can protect the qubit state from decay and decoherence more effectively than the intuitively obvious alternative, which is to fix the resonance well within a forbidden band gap of the reservoir spectrum, as far as possible from the continuum edge. The " counterintuitive" nonadiabatic method outlined here can outperform its adiabatic counterparts in maintaining a high fidelity of quantum logic operations. The remarkable effectiveness of the proposed method, which requires much lower rates of frequency changes than previously proposed control methods, is due to the ability of appropriately alternating detunings from the continuum edge to augment the interference of the emitted and backscattered quanta, thereby helping to stabilize the qubit state against decay. Applications to the control of decay and decoherence near the edge of radiative, vibrational, and photoionization continua are discussed.

We study the giant Kerr nonlinear interaction between two ultraweak optical fields in which the cross-phase-modulation is not accompanied by spectral broadening of the interacting pulses. This regime is realizable in atomic vapors, when a weak probe pulse, upon propagating through the electromagnetically induced transparency (EIT) medium, interacts with a signal pulse that is dynamically trapped in a photonic band gap created by spatially periodic modulation of its EIT resonance. We find that large conditional phase shifts and entanglement between the signal and probe fields can be obtained with this scheme. The attainable π phase shift, accompanied by negligible absorption and quantum noise, is shown to allow a high-fidelity realization of the controlled-phase universal logic gate between two single-photon pulses.

A scalable multiatom entangled system, capable of high-performance quantum computations, can be realized by resonant dipole-dipole interacting dopants in a solid state host. In one realization, the qubits are represented by ground and subradiant states of effective dimers formed by pairs of closely spaced two-level systems (TLS). Such qubits are highly robust against radiative decay. The two-qubit entanglement in this scheme relies on coherent excitation exchange between the dimers by external laser fields. This scheme is challenging because of the nanosize control and addressability it requires. Another realization involves dipole-dipole interacting TLS whose resonance frequency lies in a photonic band gap of a dielectric photonic crystal. A sequence of abrupt changes of the resonance frequency can produce controlled entanglement (logic gates) with improved protection from radiation decay and decoherence.

We derive and investigate an expression for the dynamically modified decay of states coupled to an arbitrary continuum. This expression is universally valid for weak temporal perturbations. The resulting insights can serve as useful recipes for optimized control of decay and decoherence.

Keywords: decoherence; quantum information processing; errors correction codes; quantum Zeno and anti-Zeno effects; Josephson junction qubits; degenerate ground-state systems; optically-manipulated atoms; photonic band gap; nonadiabatic periodic dynamics; quantum memory; collective multiatom states; equivalent storage classes; decoherence free subspaces

We present an example of a situation where Fermi's golden rule does not apply, even if an unstable quantum system decays exponentially. The work is inspired by the recent experiments by Chatzidimitriou-Dreismann and co-workers on reduction of the neutron Compton scattering cross-section in hydrogenated compounds. Although full quantitative explanation of these experimental results is still to be accomplished, our preliminary results show a possibility of strong modification of the scattering cross-section.

Decay acceleration by frequent measurements (interruptions of the coupling), known as the anti-Zeno effect is argued to be much more ubiquitous than its inhibition in one- or two-level systems coupled to reservoirs (continua). In multilevel systems, frequent measurements cause accelerated decay by destroying the multilevel interference, which tends to inhibit decay in the absence of measurements.

### 2004

Giantly enhanced cross-phase modulation with suppressed spectral broadening is predicted between optically induced dark-state polaritons whose propagation is strongly affected by photonic bandgaps of spatially periodic media with multilevel dopants. This mechanism is shown to be capable of fully entangling two single-photon pulses with high fidelity.

We investigate the scattering threshold and cavity-enhanced gain in nonlinear spheres with second- or third-order permeability. Pairs of pump-driven idler and signal modes are considered, satisfying morphology-dependent resonance conditions. The thresholds and gain coefficients of amplified and stimulated Raman scattering, parametric downconversion, and analogous parametric processes in microspheres are derived and evaluated under typical conditions. Applications may include the measurement of chemical impurity concentrations or the creation of low-threshold optical parametric amplifiers using microspheres.

The development of a unified theory of dynamically suppressed and decoherence by external fields in qubits coupled to arbitrary thermal baths and dephasing sources was discussed. A driven two-level system (TLS) undergoing decay into a finite-temperature bath and while its resonant frequency and dipolar coupling to the bath were dynamically modulated by external fields, was utilized for the study. A differential mass equation (ME) for the density operator of the system was derived using Zwanizig's projection-operator technique. The results indicate that the ultrafast modulations give rise to antiresonant effects.

We show that electromagnetically-induced isotropic dipole-dipole interactions in a spin-polarized non-degenerate fermionic gas can cause an extremely exothermic phase transition, analogous to the isothermal collapse in gravitationally interacting star clusters. This collapse may result in fragmentation of the gas into a hot "halo" and a highly degenerate "core". Possible realization is envisaged in microwave-illuminated fermionic molecular gases at microkelvin temperatures.

A method to treat macroscopic quantum tunneling (MQT) by controlling it dynamically was discussed. The methods showed that decay modifications reminiscent of the quantum Zeno effect (QZE) and anti-Zeno effect (AZE) that coupled to the continuum through macroscopic quantum tunneling were realiazable for macroscopic quantum states. The MQT were dynamically controlled at low temperatures. The high-sensitivity of the dynamics and the modification of the decay rate to moderate changes were also elaborated.

We study a gaseous atomic Bose-Einstein condensate with laser-induced dipole-dipole interactions using the Hartree-Fock-Bogoliubov theory within the Popov approximation. The dipolar interactions introduce long-range atom-atom correlations which manifest themselves as increased depletion at momenta similar to that of the laser wavelength, as well as a 'roton' dip in the excitation spectrum. Surprisingly, the roton dip and the corresponding peak in the depletion are enhanced by raising the temperature above absolute zero.

We present a brief review of our recent results concerning non-mean-field effects of laser-induced dipole-dipole interactions on static and dynamical properties of atomic Bose-Einstein condensates.

We introduce and discuss two schemes for generation and transfer of photon-photon and atom-atom entanglement. First we propose a method to achieve a large conditional phase shift of a probe field in the presence of a single-photon control field whose carrier frequency is within the photonic band gap created by spatially-periodic modulation of the electromagnetically induced transparency resonance. Then we present the concept of a reversible transfer of the quantum state of two internally-translationally entangled fragments, formed by molecular dissociation, to a photon pair. Our scheme allows, in principle, high-fidelity state transfer from the entangled dissociated fragments to light, thereby producing a highly correlated photon pair. This process can be followed by its reversal at a distant node of a quantum network resulting in the recreation of the original two-fragment entangled state. The proposed schemes may have advantageous applications in quantum teleportation, cryptography, and quantum computation.

### 2003

A report on the proposal focusing on transitional entanglement of dipole-dipole interacting atoms in optical lattices was presented. Laser-induced dipole-dipole interactions were held responsible for the entanglement of atom pairs, which were confined to adjacent sites of two mutually shifted optical lattices. The modification of Einstein-Podolsky-Rosen (EPR) state by lattice-diffraction effects were also explained.

A study was performed on inversionless free-electron laser having a drift region consisting of two magnets. The numerical simulations of electron motion inside wigglers and the drift region were performed. It was found that this system has a positive mean gain over the entire energy distribution of the electron beam.

The use of off-resonant lasers to induce long-range dipole-dipole interactions whose characteristic length is the laser wavelength was proposed. These interactions can cause laser-induced "self-gravity" in a Bose Einstein condensate (BEC), leading to three-dimensional self-trapping and electrostriction accompanied by unusual excitation spectra, as well as "supersolid" structures. This paper aims to explore how the excitation spectrum and the correlations of a gaseous BEC are changed when the interatomic potential is modified via laser-induced dipole-dipole interactions.

We consider a gaseous atomic Bose-Einstein condensate with dipole-dipole interactions induced by a far off-resonance laser. The long-range dipolar interactions introduce atom-atom correlations on the new scale of the laser wavelength, giving a controllable method of squeezing low energy modes. At high enough laser intensities the correlations lead to a roton minimum in the excitation spectrum.

We propose two alternative scheme for highly efficient nonlinear interaction between weak optical fields. The first scheme is based on the attainment of electromagnetically induced transparency simultaneously for two fields via transitions between magnetically split F = 1 atomic sublevels, in the presence of two driving fields. The second scheme relies on simultaneous electromagnetically- and self-induced transparencies of the two fields. Thereby, equal slow group velocities and giant cross-phase modulation of the weak fields over long distances are achieved.

The unexplored possibility of probing and exploiting the quantum information associated with internal-translational entanglement in molecular dissociation is proposed. In principle, the scheme allows high-fidelity state transfer from the entangled dissociated fragments to light, thus producing a highly correlated photon pair.

### 2002

Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized "bullets" propagating at photonic-bandgap frequencies. Such modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.

The impediment towards the successful development of the field of quantum information (QI) is decoherence, i.e., the loss of entanglement by the effect of the environment on the systems of interest. An important challenge is that of QI engineering, by entanglement and decoherence control, in complex systems, such as unimolecular and bimolecular systems, that can simultaneously handle large amounts of QI. Progress towards this goal can be achieved by: (a) decay modification and decoherence suppression in molecules, using laser-induced phase and amplitude modulation of rovibrational levels and inter-mode couplings; (b) transfer of internal-translational entanglement and teleportation of wavepackets via molecular dissociation and collisions.

We predict the existence of a new type of spatiotemporal soliton (so-called light bullets) in twodimensional self-induced-transparency media with refractive-index modulation in the direction transverse to that of pulse propagation. These self-localized guided modes are found in an approximate analytical form. Their existence and stability are confirmed by numerical simulations, and they may have advantageous properties for signal transmission.

We propose a simple scheme for highly efficient nonlinear interaction between two weak optical fields. The scheme is based on the attainment of electromagnetically induced transparency simultaneously for both fields via transitions between magnetically split F=1 atomic sublevels, in the presence of two driving fields. Thereby, equal slow group velocities and symmetric cross coupling of the weak fields over long distances are achieved. By simply tuning the fields, this scheme can either yield giant cross-phase modulation or ultrasensitive two-photon switching.

We show that the dipole-dipole interatomic forces induced by an off-resonant running laser beam can lead to a self-bound pencil-shaped Bose condensate, even if the laser beam is a plane wave. For an appropriate laser intensity the ground state has a quasi-one-dimensional density modulation—a Bose-Einstein “supersolid”.

We survey basic quantum optical processes that undergo modifications in photonic crystals doped with resonant atoms: (a) Solitons and multi-dimensional localized "bullets" propagating at photonic band gap frequencies. These novel entities differ substantially from solitons in Kerr-nonlinear photonic crystals. (b) Giant photon-photon cross-coupling that can give rise to fully entangled two-photon states. We conclude that doped photonic crystals have the capacity to form efficient networks for high-fidelity classical and quantum optical communications.

We propose a realization of a scalable, high-performance quantum processor whose qubits are represented by the ground and subradiant states of effective dimers formed by pairs of two-level systems coupled by resonant dipole-dipole interaction. The dimers are implanted in low-temperature solid host material at controllable nanoscale separations. The two-qubit entanglement either relies on the coherent excitation exchange between the dimers or is mediated by external laser fields.

The modification of the properties of a Bose-Einstein or a Fermi-Dirac atomic gas due to laser-induced dipole-dipole interactions between the atoms are considered. Nearly-isotropic illumination of the sample by spectrally-fluctuating laser beams averages out the static r(-3) dipole-dipole interaction, leaving the retarded r(-1) "self-gravitating" attraction in the near zone. The analogies of ultracold many-atom systems, self-bound by such laser-induced "gravity", with compact stars ("Bose stars" or "White Dwarfs") are emphasized. Even a single plane-wave laser induces dipole-dipole interactions capable of causing a cigar-shaped Bose condensate to exhibit self binding and density modulations.

### 2001

We consider a trapped cigar-shaped atomic Bose-Einstein condensate irradiated by a single far-off resonance laser polarized along the cigar axis. The resulting laser-induced dipole-dipole interactions between the atoms significantly change the size of the condensate, and can even cause its self-trapping.

An expression for the dynamically modified decay of states coupled to an arbitrary continuum was investigated and derived. The derived expression was found to be valid for weak temporal perturbations. It was shown that the resulting insights can serve as a general recipe for optimized decay and decoherence suppression for quantum logic operations or decay enhancement for the control of chaos or chemical reactions.

We investigate the collective excitations of an atomic Bose-Einstein condensate in the self-binding regime produced by electromagnetically induced "gravity" (1/r attraction). Analytical expressions for the frequencies of the monopole and quadrupole modes are obtained at zero temperature, using the sum-rule approach, and compared with the exact results available in the Thomas-Fermi limit. The low-energy dynamics of such condensates is shown to be dominated by the effective "plasma" frequency. An analog of the Jeans gravitational instability is analyzed.

Interference in free electron laser (FEL) was analyzed to study the broadband optical gain of an optically dispersive interface region in FEL. The dynamics of an electron interacting with laser field in optical wiggler was presented to determine the small-signal gain in two interfering wigglers. The electron drift between the wigglers in dispersive regions of an optical klystron acquired a phase shift relative to the ponderomotive potential with an increase in the deviation of electron velocity. The analysis suggested universal dependence of broadband gain on optical dispersion.

The possibility of realizing photon-photon nonlinear phase shifters and switches with a potentially very high efficiency and without external laser fields in photonic crystals (PCs) doped at a low concentration with four-level atoms is illustrated. These atoms have two transitions tuned to two incident photons and an intermediate transition tuned to a singular feature of the structured density of modes (DOM) spectrum of the PC. These features have unique advantages for quantum information applications.

Cold diatomic molecules are analyzed as a source of atom pairs. The dissociation of these molecules are investigated. The atoms pairs have highly correlated positions and momenta. The collision with one of the EPR correlated atoms and manipulation of the other atom in the pair can cause wave packet teleportation.

Novel regimes of probe scattering by atoms trapped in optical lattices in the random-density and multiple-scattering regimes were identified. These regimes were characterized by a universal feature of large density fluctuations.

We consider the influence of refractive index fluctuations (due to randomly distributed inclusions inside a dielectric spherical droplet) on the. line shapes of scattering Mie resonances. The significant difference in the spatial distributions of the mode functions participating in the process does not allow one to employ the standard statistical ensembles used in random matrix theory. We propose to model the system by a simplified random ensemble which gives a very good agreement with the available experimental data, and we predict a type of line shape for narrow scattering resonances.

In our recent publication [D. O'Dell et al., Phys. Rev. Lett. 84, 5687 (2000)] we proposed a scheme for electromagnetically generating a self-bound Bose-Einstein condensate with 1/r attractive interactions: the analog of a Bose star. Here we focus upon the conditions necessary to observe the transition from external trapping to self-binding. This transition becomes manifest in a sharp reduction of the condensate radius and its dependence on the laser intensity rather than the trap potential.

We discuss a simple, experimentally feasible scheme, which elucidates the principles of controlling the reservoir spectrum and the spectral broadening incurred by repeated measurements. This control can yield either the inhibition (Zeno effect) or the acceleration (anti-Zeno effect) of the quasiexponential decay of the observed state by means of frequent measurements. In the discussed scheme, a photon is bouncing back and forth between two perfect mirrors, each time passing a polarization rotator. The horizontal and vertical polarizations can be viewed as analogs of an excited and a ground state of a two level system (TLS). A polarization beam splitter and an absorber for the vertically polarized photon are inserted between the mirrors, and effect measurements of the polarization. The polarization angle acquired in the electrooptic polarization rotator can fluctuate randomly, e.g., via noisy modulation. In the absence of an absorber the polarization randomization corresponds to TLS decay into an infinite-temperature reservoir. The non-Markovian nature of the decay stems from the many round trips required for the randomization. We consider the influence of the polarization measurements by the absorber on this non-Markovian decay, and develop a theory of the Zeno and anti-Zeno effects in this system.

The quantum Zeno effect (QZE) is the striking prediction that the decay of any unstable quantum state can be inhibited by sufficiently frequent observations (measurements). The consensus opinion has upheld the QZE as a general feature of quantum mechanics which should lead to the inhibition of any decay. The claim of QZE generality hinges on the assumption that successive observations can in principle be made at time intervals too short for the system to change appreciably. However, this assumption and the generality of the QZE have scarcely been investigated thus far. We have addressed these issues by showing that (i) the QZE is principally unattainable in radiative or radioactive decay, because the required measurement rates would cause the system to disintegrate; (ii) decay acceleration by frequent measurements (the anti-Zeno effect - AZE) is much more ubiquitous than its inhibition. The AZE is shown to be observable as the enhancement of tunneling rates (e.g., for atoms trapped in ramped-up potentials or in current-swept Josephson junctions), fluorescence rates (e. g., for Rydberg atoms perturbed by noisy optical fields) and photon depolarization rates (in randomly modulated Pockels cells).

### 2000

Novel methods are discussed for the state control of atoms coupled to single-mode and multi-mode cavities and microspheres. (1) Excitation decay control: The quantum Zeno effect, i.e. inhibition of spontaneous decay by frequent measurements, is observable in high-Q cavities and microspheres using a sequence of evolution-interrupting pulses or randomly-modulated CW fields. By contrast, in 'bad' cavities or open space, frequent measurements can only accelerate the decay, causing the anti-Zeno effect. (2) Location-dependent interference of decay channels: Control of two metastable states is feasible via resonant single-photon absorption to an intermediate state, by engineering spontaneous emission in a multimode cavity. (3) Decoherence control by conditionally interfering parallel evolutions: An arbitrary internal state of an atomic wavepacket can be protected from decoherence by interference of its interactions with the cavity over many different time intervals in parallel, followed by the detection of appropriate atomic-momentum observables. The arsenal of control methods described above can advance the state-of-the-art of quantum information storage and manipulation in cavities.

We consider a scheme of two noncollinear wigglers with an intermediate magnetic drift region, constituting a free-electron laser without inversion (FELWI). Two mechanisms of phase shifts in the drift region between the wigglers owing to a series of magnetic lenses can give rise to FELWI: velocity- and angle-dependent shifts. An appropriate combination of these shifts is shown to provide the conditions for amplification without inversion. The phase shifts optimizing the gain are found. A specific scheme for the drift region is suggested.

The existence of multidimensional solitons localized in both space and time are predicted in two- and three-dimensional self-induced-transparency media embedded in a Bragg grating. These light bullets were found to be stable. Such stability suggest new possibilities of signal transmission control and self-trapping of light.

We show that the fidelity of teleportation of continuous quantum variables can be improved by conditional photon-number measurement of the entangled state. Further, we propose a teleportation scheme based on photon counting on the output fields of a squeezer that combines the mode whose quantum state is desired to be teleported and one mode of the two-mode squeezed vacuum playing the role of the entangled state.

We demonstrate that interference of evolutions (interaction 'histories') is realizable for two entangled systems, such as a two-level atom coupled to a cavity field over many different time intervals in parallel. Such interference is conditional upon the detection of appropriate atomic momentum observables. It allows us to fully control and manipulate any state of both entangled systems. The sense of evolution (towards the 'past' or 'future') is also controlled by this method. In the case of a multi-mode field it allows us to protect any state of the two-level atom (qubit) from decoherence, caused by entanglement with the field. The success probability of this control method can be optimized. Several schemes for realizing this method are suggested.

We show that the recently proposed scheme of teleportation of continuous variables [S.L. Braunstein and H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998)] can be improved by a conditional measurement of the entangled state shared by the sender and the recipient. The conditional measurement subtracts photons from the original entangled two-mode squeezed vacuum, by transmitting each mode through a low-reflectivity beam splitter and performing a joint photon-number measurement on the reflected beams. In this way the degree of entanglement of the shared state is increased and so is the fidelity of the teleported state.

“Light bullets” are multidimensional solitons which are localized in both space and time. We show that such solitons exist in two- and three-dimensional self-induced transparency media and that they are fully stable. Our approximate analytical calculation, backed and verified by direct numerical simulations, yields the multidimensional generalization of the one-dimensional sine-Gordon soliton.

It is shown that the quantum Zeno effect, i.e., inhibition of spontaneous decay by frequent dephasing (measurements), is observable only in spectrally finite reservoirs, e.g., in cavities, using a sequence of evolution-interrupting pulses or randomly-modulated CW fields. By contrast, non-destructive measurements can only accelerate decay in free space, via the anti-Zeno effect.

We address several generic quantum optical processes that undergo basic modifications in photonic crystals: (a) spontaneous formation of atomic coherence; (b) two-photon binding and entanglement; (c) self-induced transparency and gap solitons.

We examine several proposed schemes by Franson et al. for quantum logic gates based on non-local exchange interactions between two photons in a medium. In these schemes the presence of a single photon in a given mode is supposed to induce a large phase shift on another photon propagating in the same medium. We conclude that the schemes proposed so far are not able to produce the required conditional phase shift, even though the proposals contain many stimulating and intriguing ideas.

We show that particular configurations of intense off-resonant laser beams can give rise to an attractive 1/r interatomic potential between atoms located well within the laser wavelength. Such a “gravitational-like” interaction is shown to give stable Bose-Einstein condensates that are self-bound (without an additional trap) with unique scaling properties and measurably distinct signatures.

### 1999

We show that optical tachyonic dispersion corresponding to superluminal (faster-than-light) group velocities characterizes parametrically amplifying media. The turn-on of parametric amplification in finite media, followed by illumination by spectrally narrow probe wavepackets, can give rise to transient tachyonic wavepackets. In the stable (sub-threshold) operating regime of an optical phase conjugator, it is possible to transmit probe pulses with a superluminally advanced peak, whereas conjugate reflection is always subluminal. In the unstable (above-threshold) regime, superluminal response occurs both in reflection and in transmission, at times preceding the onset of exponential growth due to the instability. Remarkably, the quantum information transmitted by probe or conjugate pulses, albeit causal, is confined to times corresponding to superluminal velocities. These phenomena are explicitly analyzed for four-wave mixing, stimulated Raman scattering and parametric downconversion.

We point out that the quantum Zeno effect, i.e., inhibition of spontaneous decay by frequent measurements, is observable only in spectrally finite reservoirs, i.e., in cavities and waveguides, using a sequence of evolution-interrupting pulses or randomly-modulated CW fields. By contrast, such measurements can only accelerate decay in free space.

With the help of some remarkable examples, it is shown that conditional measurements performed on two-level atoms just after they have interacted with a resonant cavity field mode are able to recover the coherence of number-state superpositions, which is lost due to dissipation.

The injection of spectrally narrow probe wavepackets into quantized parametrically amplifying media can give rise to transient tachyonic wavepackets. Remarkably, their quantum information, albeit causal, is confined to times corresponding to superluminal velocities, which is advantageous for communications.

Spontaneous decay of excited cold atoms into a cavity can drastically affect their translational dynamics, namely, atomic reflection and transmission through a potential barrier.

We put forward a method for optimized distillation of partly entangled pairs of quantum bits into a smaller number of more entangled pairs by recurrent local unitary operations and projections. Optimized distillation is achieved by minimization of a cost function with up to 30 real parameters, which is chosen to be sensitive to the fidelity and the projection probability at each step. We show that in many cases this approach can significantly improve the distillation efficiency in comparison to the present methods.

We consider an optical medium consisting of a periodic refractive-index grating and a periodic set of thin layers of two-level systems resonantly interacting with the electromagnetic field. Recently, it has been shown that such a system gives rise to a vast variety of stable bright solitons. In this work, we demonstrate that the system has another very unusual property: stable bright solitons can coexist with stable continuous-wave (cw) states and stable dark solitons (DS’s). Depending on the parameters’ values, a DS frequency band coexists (without overlap) with one or two bright-soliton bands. Quiescent (standing) DS’s are found in an analytical form, and moving ones are obtained numerically. Simulations show that a considerable part of the DS solutions are completely stable against arbitrary small perturbations. The fact that this system supports both stable bright and dark solitons for the same parameters values may find interesting applications in photonics.

We propose a scheme which can effectively restore fixed points in the quantum dynamics of repeated Jaynes-Cummings interactions followed by atomic state measurements, when the interaction times fluctuate randomly. It is based on selection of superposed atomic states whose phase correlations tend to suppress the phase fluctuations of each separate state. One suggested realization involves the convergence of the cavity field distribution to a single Fock state by conditional measurements performed on two-level atoms with fluctuating velocities after they cross the cavity. Another realization involves a trapped ion whose internal-motional state coupling fluctuates randomly. Its motional state is made to converge to a Fock state by conditional measurements of the internal state of the ion.

We show that giant quasibound diatomic complexes, whose size is typically hundreds of nm, can be formed by intracavity cold diatom photoassociation or photodissociation in the strong atom-cavity coupling regime.

We study the use of the Faraday effect as a quantum clock for measuring traversal times of evanescent photons through magnetorefractive structures. The Faraday effect acts both as a phase shifter and as a filter for circular polarizations. Only measurements based on the Faraday phase-shift properties are relevant to the traversal time measurements. The Faraday polarization filtering may cause the loss of nonlocal (Einstein-Podolsky-Rosen) two-photon correlations, but this loss can be avoided without sacrificing the clock accuracy. We show that a mechanism of destructive interference between consecutive paths is responsible for superluminal traversal times measured by the clock.

### 1998

We present hitherto unknown forms of soliton dynamics in the forbidden frequency gap of a Bragg reflector, modified by periodic layers of near-resonant two-level systems (TLS). Remarkably, even extremely low TLS densities create an allowed band within the forbidden gap. This spectrum gives rise, for any Bragg reflectivity, to a vast family of stable gap solitons, both standing and moving, having a unique analytic form, an arbitrary pulse area, and inelastic collision properties. These findings suggest new possibilities of transmission control, noise filtering, or “dynamical cavities” (self-traps) for both weak and strong signal pulses.

We demonstrate the possibility of simply and effectively controlling the inversionless gain between two excited states in a ladder configuration, by injecting atoms (molecules) into a cavity. The control is effected by the cavity-mode decay rate and vacuum Rabi frequency, chosen according to the decay and dephasing rates of the upper and lower states. The analogy with the control of inversionless gain by a classical strong field is discussed. This scheme is expected to be robust under conditions of thermal equilibrium or non-selective pumping of excited states.

We show that the injection of spectrally narrow probe wave packets into quantized parametrically amplifying media can give rise to transient tachyonic wave packets. Remarkably, their quantum information, albeit causal, is confined to times corresponding to superluminal velocities, which is advantageous for communications. These phenomena are explicitly analyzed for stimulated Raman scattering, parametric down-conversion and four-wave mixing.

Novel methods are discussed for the state control of atoms coupled to multi-mode reservoirs with non-Markovian spectra: 1) Excitation decay control: we point out that the quantum Zeno effect, i.e., inhibition of spontaneous decay by frequent measurements, is observable in open cavities and waveguides using a sequence of evolution-interrupting pulses or randomly-modulated CW fields. 2) Location-dependent interference of decay channels - nonadiabatic (resonant) control: We show that the control of populations and coherences of two metastable states is feasible via resonant single-photon absorption to an intermediate state, by controlled spontaneous emission in a cavity. 3) Decoherence control by conditionally interfering parallel evolutions: We demonstrate that an arbitrary internal atomic state can be completely protected from decoherence by interference of its interactions with the reservoir over many different time intervals in parallel. Such interference is conditional upon the detection of appropriate atomic-momentum observables. Realization in cavities is suggested. The rich arsenal of control methods described above can improve the performance of single-atom devices. It can also advance the state-of-the-art of quantum information encoding and processing.

We theoretically analyze wave packet transmission through a phase-conjugating mirror and show that the transmission of a suitably chosen input pulse is superluminal, i.e. the peak of the pulse emerges from the mirror before the time it takes to travel the same distance in vacuum. This pulse reshaping effect can be attributed directly to the dispersion relation in the nonlinear medium constituting the mirror. Thus, for the first time a connection is laid between optical phase conjugation and superluminal behavior. In view of its additional amplifying ability, a phase-conjugating mirror is a most promising candidate for an experimental observation of tachyonic signatures.

We show that conditional measurements on atoms following their interaction with a resonant cavity field mode can be used to effectively counter the decoherence of Fock-state superpositions due to cavity leakage.

We theoretically investigate the response of optical phase conjugators to incident probe pulses. In the stable (subthreshold) operating regime of an optical phase conjugator it is possible to transmit probe pulses with a superluminally advanced peak, whereas conjugate reflection is always subluminal. In the unstable (above-threshold) regime, superluminal response occurs both in reflection and in transmission, at times preceding the onset of exponential growth due to the instability.

Spontaneous decay of excited cold atoms into a cavity can drastically affect their translational dynamics, namely, atomic reflection, transmission and localization at the interface. We show that the quantum Zeno effect on excitation decay of an atom is observable in open cavities and waveguides, using a sequence of evolution-interrupting pulses on a nanosecond scale.

We propose a method which can effectively stabilize fixed points in the classical and quantum dynamics of a phase-sensitive chaotic system with feedback. It is based on feeding back a selected quantum subensemble whose phase and amplitude stabilize the otherwise chaotic dynamics. Although the method is rather general, we apply it to realizations of the inherently chaotic Ikeda map. One suggested realization involves the Mach-Zender interferometer with Kerr nonlinearity. Another realization involves a trapped ion interacting with laser fields.

Remarkable quantum effects are predicted for an initially excited two-level wave packet incident on a broadband vacuum-field reservoir with sharp spatial boundaries: (a) reflection of the excited wave packet from the boundary (skin effect); (b) transient three-dimensional binding of the decayed wave packet to the boundary by photons carrying more energy than the incident wave packet. These effects are realizable for cold atoms in cavities where excitation decay is nearly exponential but strongly enhanced.

### 1997

Spontaneous decay of excited cold atoms into cavity can drastically affect their translational dynamics, namely, atomic reflection, transmission or localization in the cavity.

### 1996

We put forward a theory of excitation decay in two-level atoms that tunnel through a square potential barrier while spontaneously emitting photons into an effectively one-dimensional mode continuum. The resulting decoherence can exponentially enhance the total tunneling probability. This enhancement is due to atoms whose final kinetic energy is raised above the barrier by the emission of photons detuned below resonance.

Quantum theory is applied to interference of emission and absorption in a two-section Cerenkov free-electron laser (FEL). A scheme for absorption cancellation with enhanced gain, which resembles ''lasing without inversion'' in atomic systems, is proposed. This scheme is based on the adjustment of the phases of electrons and light by appropriate dispersion between the two sections. It enables FEL operation even with a broad electron momentum spread. Such a scheme is interesting in the context of EEL operation in the ultraviolet and X-ray regimes.

A two-stage free-electron laser with a specially designed delay of electrons in the drift region between the two wigglers allows us to obtain essentially positive gain as a function of detuning, i.e., "lasing without inversion" (LWI). The key physical assumption is that it is possible to tell which electrons emit and which absorb laser energy. We here show that straightforward attempts to realize LWI operation in a free-electron laser are frequently (but not inevitably) frustrated by the difficulty of telling the difference between emitting and absorbing electrons. We propose a scheme utilizing both transverse and longitudinal components of the electron velocity to achieve cancellation of absorption. Numerical simulations verifying the validity of the scheme are presented.

Superluminal peak-traversal times of evanescent photonic wavepackets in dielectric structures are shown to result from destructive interference between waves which traverse multiple paths corresponding to successive causal time-delays. Information is shown to be transmitted always causally and only by non-analytic disturbances. EPR correlations between two photons are diminished if the photon traversing a structure is split between distinguishable paths on which the polarization vector is rotated proportionally to the path length.

A mechanism for controlling arbitrary quantum-field states in a cavity is proposed. It is based on a single conditional measurement of the state of a two-level atom, following a periodic sequence of field-atom couplings with alternating near-resonant and off-resonant detunings. The resulting field state is controlled by the arbitrarily large number of parameters that characterize the sequence of detunings.

We survey our recent results on the modifications of optical processes by field confining structures.

A system of two identical atoms sharing a photon with a high-[Formula Presented] resonator mode is studied by a nonperturbative formalism. As opposed to previously considered models, here the interatom coupling is shown to result from competing effects of vacuum Rabi splitting and photon exchange via off-resonant modes. Strong suppression of interatom excitation transfer is predicted at both near- and far-zone separations.

Keywords: Optics; Physics, Applied

We identify the universal mechanism that is responsible for superluminal (faster-than-light) traversal times as well as the narrowing of wave packets transmitted through various nondissipative media. This mechanism is shown to be predominantly destructive interference between successive wave-packet components traversing all accessible causally retarded paths. It strongly depends on wave-packet coherence and width, and can cause superluminal traversal not only in evanescent-wave “tunneling” but also in allowed propagation.

A unified theory of two-level atom coupling to vacuum field reservoirs with arbitrary mode-density spectra is used to demonstrate that the quantum Zeno effect on excitation decay of the atom (and, correspondingly, inhibition of spontaneous emission) is observable in open cavities and waveguides, using a sequence of evolution-interrupting pulses on a nanosecond scale.

We establish a quantum theory of gap solitons in a one-dimensional periodic dielectric structure [distributed Bragg reflector (DBR)] of a Kerr nonlinearity. The electromagnetic field in the structure is quantized within the two-band approximation. The basic idea for this quantization is that incident photons with frequencies in the band gap of the DBR are scattered into the upper “conduction” and lower “valence” bands by the nonlinearity. The effective Hamiltonian of quantum gap solitons is derived within the effective-mass regime. The eigenstates of the Hamiltonian are constructed exactly by Bethe’s ansatz method. We find that in certain band gaps of the DBR these eigenstates can be bound, consisting of one or more photon pairs from the conduction and valence bands. These bound multiphoton states are optical analogs of exciton molecules [optical multiexcitons (OMEs)]. Their existence should be manifested by the discrete spectrum of band-gap transmission as a function of the transmitted photon number and by the multiexponential falloff of intensity-intensity correlations on a 0.1-mm scale. Quantum gap solitons are shown to arise as superpositions of OMEs whenever the nonlinear binding exceeds phonon scattering.

A Reply to the Comment by Qianbing Zheng, Takayoshi Kobayashi, and Takashi Sekiguchi.

Electromagnetic fields dressed by inverted two-level atoms become tachyonlike excitations with group velocities which are faster than c, infinite, or negative. Such excitations describe the stable modes of the medium when it is weakly probed off resonance. The launching of these tachyonlike excitations is discussed, along with a proposed experiment to observe them. Their existence does not violate Einstein causality.

We show that by combining nonselective and conditional measurements on a sequence of excited two-level atoms traversing a resonant cavity, one can construct a practical strategy for compressing an arbitrary photon-number distribution (thermal distributions included) into a desired Fock state with high probability of success and low number of measurements.

We introduce a general strategy for preparation of arbitrary quantum states via optimal control of repeated conditional measurements. The effectiveness of this strategy in generating finite Fock-state superpositions with a high level of confidence from experimentally accessible coherent states is demonstrated for the simple and well known Jaynes-Cummings model dynamics.

We investigate the resonant interaction of a dipolar j=0⇆j=1 angular-momentum transition with the quantized field in a dielectric sphere. New features arise on account of the degeneracy of atomic levels and field modes with low azimuthal angular momentum, in slightly deformed spheres (oblate spheroids). For TE-mode excitation we obtain the dynamics of a degenerate Λ or V configuration with the usual coherent-state collapse and revivals. For TM-mode excitation new behavior is found: due to interference between σ- and π-polarized transitions, which can be controlled by the atomic position and/or dipole orientation, coherent-state revivals and the corresponding atom-field energy exchange may be suppressed or delayed.

### 1995

We present a classical approach to free-electron lasers without inversion. The destructive interference of absorption in two sequential interaction regions (wigglers) results in absorption cancellation and strongly enhanced gain. Appropriately designed magnetic fields between the two interaction regions separate emitting and absorbing electrons and adjust their oscillation phases in the two interaction regions according to their velocities. In this way the adverse effects of wide (inhomogeneous) electron velocity spread are negated, and most of the inhomogeneous distribution contributes to emission rather than absorption. This scheme does not require momentum bunching (population inversion) to ensure highly efficient operation.

We analyze the near-resonant interaction between a two-level atom with resonance frequency in a photonic band gap and a local-defect field mode with initially thermal or Poissonian photon statistics. Whereas spontaneous decay is forbidden in this case, atomic states dressed by the defect field can decay via coupling to the mode continuum outside the band gap. Remarkably, the resulting non-Markovian cascade of dressed states transitions can lead to the accumulation of nearly all of the initial photon-number distribution in a single Fock state, upon measuring the excitation of the atom emerging from the structure. Under certain conditions, such a measurement can yield a correlated combination of two adjacent Fock states, which reflects the initial coherence in either the atom or the field. Another striking coherence effect is the non-decaying oscillation (as a function of interaction time) exhibited by Fock-state populations prepared by measuring the final atomic state.

We present a universal mechanism which allows us to relinquish momentum population inversion in free-electron lasers, and extract strongly enhanced gain from a broad momentum distribution. This is achievable by appropriately designed magnetic fields between two sequential interaction regions, which cause, purely classically, absorption cancellation (by destructive interference) and emission enhancement (by constructive interference).

We find a Bethe-ansatz solution for pairwise interacting quanta within the effective-mass regime of band-gap propagation in nonlinear Bragg reflectors. Our theory predicts a new kind of collective excitation of the electromagnetic field dressed by such media, namely, optical multiexciton (OME) complexes (or condensates), which are quantum states associated with gap solitary waves. Their existence should be manifested by the discrete spectrum of band-gap transmission as a function of the transmitted photon number and by the multiexponential falloff of intensity-intensity correlations on a 0.1 mm scale. OMEs should have advantageous stability properties.

We show that pulse transmission through near-resonant media embedded within periodic dielectric structures can produce self-induced transparency (SIT) in the band gap of such structures. This SIT constitutes a principally new type of gap soliton.

### 1994

We present a comprehensive quantum electrodynamical analysis of the interaction between a continuum with photonic band gaps (PBGs) or frequency cut-off and an excited two-level atom, which can be either 'bare' or 'dressed' by coupling to a near-resonant field mode. A diversity of novel features in the atom and field dynamics is shown to arise from the non-Markovian character of radiative decay into such a continuum of modes. Firstly the excited atom is shown to evolve, by spontaneous decay, into a superposition of nondecaying single-photon dressed states, each having an energy in a different PBG, and a decaying component. This superposition is determined by the atomic resonance shift, induced by the spontaneously emitted photon, into or out of a PBG. The main novel feature exhibited by the decaying excited-state component is the occurrence of beats between the shifted atomic resonance frequency and the PBG cut-off frequencies, corresponding to a non-Lorentzian emission spectrum. Secondly the induced decay of a resonantly driven atom into such a continuum exhibits a cascade of transitions down the ladder of dressed states, which are labelled by decreasing photon numbers of the driving mode. Remarkably, this cascade is terminated at the dressed-state doublet, from which all subsequent transitions to lower doublets are forbidden because they fall within the PBG. This doublet then becomes an attractor state for the populations of higher-lying doublets. As a result, the photon-number distribution of the driving mode becomes strongly sub-Poissonian.

A general analysis of an oscillator with periodic frequency modulation is given. It is shown that squeezing and excitation energy exponentially grow with the number of modulation cycles under the condition of parametric instability. This condition yields a prescription for maximized squeezing when the frequency is periodically swept in an adiabatic fashion, with an abrupt return to the initial frequency at the end of each period. The type of modulation considered is shown to have remarkably broad instability domains near arbitrarily high ratios of the oscillator period to the modulation cycle duration. This property stands in striking contrast to the rapid narrowing of the squeezing domains with the ratio of the pump frequency to that of the signal in existing parametric processes. We discuss a possible realization of the proposed scheme, based on frequency modulation of a cavity mode in the microwave domain by a periodic train of optical pulses, and show that extremely strong squeezing is feasible under rather moderate requirements.

A simple scheme is presented that allows the generation and detection of nonclassical states of the electromagnetic (em) field with controllable (predetermined) photon-number and phase distributions. It is based on the two-photon resonant interaction of a single em field mode in a high-e cavity with initially excited atoms crossing the cavity sequentially (one at a time). The sequence duration should be much shorter than the cavity-mode lifetime. Nonclassical states of the field are generated conditionally, by selecting only those sequences wherein each atom is measured to be in the excited state after the interaction. The field distribution resulting from a sequence of N such measurements is peaked about 2N positions in the phase plane, which evolve:sinusoidally as a function of the atomic transit times and are therefore simply controlled. When these peaks are chosen not to overlap, the field state constitutes a generalized Schrodinger cat. By choosing them to overlap, we can make parts of the field distribution strongly interfere, giving rise to decimation of the photon-number distribution. In particular, this process can prepare Pock states with controlled photon numbers. The generated phase distribution can be detected by monitoring the pattern of revivals in the excitation of a ''probe'' atom.

### 1993

We have investigated the spectral properties of light scattering by small dielectric spheres whose resonant modes are perturbed by disordered static scatterers placed inside. We show that: (a) A narrow peak in the scattering spectrum, which is associated with a highly degenerate Mie resonance with a surface mode, can be broadened into a nearly semicircular curve. (b) Two such adjacent peaks can become overlapping, and the resulting curve differs from the linear superposition of the two curves. (c) The scattering cross section of a resonant mode can be increased by several orders of magnitude.

A structural defect in a two-dimensionally periodic dielectric structure may form a local field mode photonic within a band gap in which no other E-polarized field modes exist. We show that such a defect mode can give rise to new quantum-electrodynamic effects in resonant field-atom interaction, owing to the spatially modu- lated standing-wave character of its field. Atomic-beam motion is considered (a) along an interplanar defect and (b) through a spherical defect. The resonant interaction of a moving two-level atom with the quantized field of these defects can yield hitherto unknown features—oscillatory patterns of the atomic population inversion, fluorescence spectra, and nonclassical field states—that are essentially different from their counterparts in the standard Jaynes-Cummings model, which holds for atomic-beam motion in a spatially uniform singlemode field.

It is shown that lasing in free-electron devices can be attained without the standard population inversion between the two portions of the electron momentum distribution that contribute to stimulated emission and absorption, respectively. Coherent superpositions of two electronic states in appropriately designed wigglers can strongly suppress stimulated absorption without hampering stimulated emission. The resulting gain curve is symmetric about the emission resonance, and yields a much larger gain than the antisymmetric gain curve of a standard free-electron laser with the same parameters.

### 1992

We put forward a simple, feasible scheme for the preparation and subsequent detection of macroscopic quantum superposition (MQS) states. It is based on the two-photon model which obtains when a cascade of two atomic transitions is resonant with twice the field frequency. The initial conditions amount to a field in a mixed state characteristic of lasers or masers and an excited atom. The MQS is generated by a conditional measurement of the atomic excitation after an interaction time that determines the relative phase of the MQS components. Remarkably, the MQS is subsequently detected and its phase is inferred by measuring the excitation probability of a second, "probe," atom, as a function of its interaction time. The realization of the scheme in the optical domain, using dielectric microspheres, is discussed.

We consider the quantum electrodynamics of an atom uniformly moving through a single spatially periodic field mode. The shape and periodicity of the field modulation can be designed by an appropriate choice of a defect in a periodic structure that possesses a forbidden spectral band (a photonic band gap). This design of the periodic modulation can improve our control over the evolution and properties (e.g., photon statistics) of nonclassical Schrödinger-cat states of the field, generated by resonant interaction with the atom.

Keywords: Optics; Physics, Multidisciplinary

### 1991

Keywords: SPONTANEOUS EMISSION; SUPER-RADIANCE; ATOMS; COLLISIONS

A system of two colliding neutral or ionized atoms with excited states that exhibit fine-structure splitting is shown to emit resonance fluorescence, the quantum features of which can reveal the collisional dynamical correlations between the atoms. Time-resolved measurements of quantum noise (squeezing properties) of the emitted field are shown to yield detailed information on the dynamical correlations. Notably, they disclose the phase between the dynamically correlated two-atom adiabatic states, which is not available from conventional spectroscopy. Such phase information can be a sensitive probe of collision dynamics. It is also important for the achievement of enhanced selectivity in laser-induced reactive collisions or dissociation, based on controllable coherent superpositions of adiabatic states.

We introduce a new approach to photodetection, based on absorbers (atoms, molecules, or dopant donors in semiconductors) that are kept in a steady superposition of two bound states having different spatial symmetries (e.g., s and p0). We consider the illumination of such absorbers by a superposition of two fields that are mutually orthogonal by virtue of polarization or frequency, and measurements of the resulting photocurrent along the direction of polarization of one of the fields. In contrast to conventional photon counters, the directional photocurrent generated in the considered scheme measures only the phase-sensitive cross products of the mutually orthogonal field amplitudes, without responding to the photon flux of each mode separately. If the light is a superposition of a one- or two-mode squeezed vacuum field and a nearly coherent (local-oscillator) field orthogonal to the former, then cross correlations between two such photocurrents yield the autocorrelation function of the squeezed-field quadrature without terms related to the noise of the local oscillator (although shot noise still affects the degree of accuracy to which the autocorrelation is measured).

It is suggested that the quantum uncertainty of cavity radiation is measurable via Aharonov-Bohm effects for electrons in a ring which is threaded by the magnetic cavity flux. When the electrons follow this oscillatory flux nearly adiabatically, and dissipation is negligible, the noise in the ring current should provide a quantum-nondemolition measure of the flux uncertainty. Unlike standard photodetection, such measurements should reveal the scaling of the flux uncertainty with the diamagnetic or dielectric index of the cavity medium, depending on the dimensions of the electron ring.

### 1990

Radiative coupling between identical atoms sharing an excitation is studied in media where dispersion creates photonic band gaps, i.e., forbidden bands of light propagation for all directions and polarizations. Photonic band gaps can exist in media whose dielectric index exhibits strong three-dimensionally periodic modulations (photonic crystals) or in bands of polaritonic media. It is shown that the resonant dipole-dipole interaction as well as cooperative fluorescence of two-atom systems can be strongly enhanced or suppressed, to the extent of being essentially eliminated, by one of the following mechanisms: (a) dependence on location of the atoms within a unit cell of a photonic crystal, i.e., sensitivity to the spatial variation of the field normal modes; (b) dependence on the density of normal modes in allowed bands and on the density of virtual (evanescent) modes in band gaps. The ability to suppress the dipole-dipole interactions at interatomic separations characterizing quasimolecules would have far-reaching implications on their dissociative or collisional dynamics, spectroscopy, and rates of energy transfer.

### 1989

We demonstrate that one can generate and control photocurrents in semiconductors, without bias voltage, through multiple-frequency phase-coherent laser excitation of donors.

Time-resolved cooperative fluorescence (TRCF) from electronically excited dissociating homonuclear diatoms is suggested as a new technique for studying orbital and spin-polarization effects in fragmented diatoms. The method is based on a theoretical prediction of a novel feature named here 'superbeats'. This feature results from a combination of two oscillatory effects, namely, the ringing oscillations caused by the time variation of the interference phase between the receding atoms during emission (P. Grangier, A. Aspect and J. Vigué, Phys. Rev. Lett., 1985, 54, 418) and the quantum beats associated with the fine-structure splitting. The time-resolved superbeat pattern is shown to be sensitive to the amplitudes and phases of the superposed states, with different orbital polarization and spin, mixed by adiabatic and non-adiabatic couplings in the outcome of the dissociation process. Quantitative estimates are made, based on a detailed analysis, for the photodissociation of Li_{2}. Under conditions in which rotational effects can be neglected, the two states ^{1}Σ_{u(g)} and ^{3}Π_{u(g)} of Li_{2} are superposed in the final outcome of the reaction. This should lead to a superbeat pattern dependent on the amplitude and phase of the superposition. Conditions for the experimental observability of these features have been studied, showing that a time resolution of ≲0.1 ns is required.

### 1988

A semiclassical theory of stimulated processes in dielectric spherical particles is formulated. The theory applies to the small-signal regime and to isotropic (but radially nonuniform) pumping. Iterative treatment of the pumped-medium susceptibility by scattering theory demonstrates the basic features observed experimentally by Chang and co-workers [H. M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 499 (1984); S. X. Qian and R. K. Chang, Phys. Rev. Lett. 56, 926 (1986)], namely, the drastic reduction of the threshold for lasing and multiorder stimulated Raman processes, and the frequency pulling from Mie resonances of the inactive medium.

We predict a new type of time-resolved cooperative fluorescence (CF) obtainable when a homonuclear alkali-metal diatom dissociating via a *1 state evolves (by nonadiabatic radial coupling) into a superposition of two excited adiabatic states correlated to different doublet levels. CF intensity then combines ringing oscillations, caused by time variation of the interference phase between the receding emitting atoms, with quantum beats associated with fine-structure splitting. The calculated CF patterns for Li2 are sensitive to the amplitudes and relative phase of the two superposed adiabatic states.

It is pointed out that the emission of photons in the GeV range produced by the annihilation of channeled positrons can be stimulated by superfluorescent emission of characteristic radiation in the MeV range from a beam of channeled electrons or positrons. The threshold current for the entire process is 1010 times lower than that of stimulated Compton scattering of visible light into the MeV range of frequencies.

This article presents a unified formulation and review of an extensive class of radiation effects and devices based on free or quasifree electrons. The effects and devices reviewed include slow-wave radiators [such as erenkov, Smith-Purcell, and TWT (traveling-wave tube) effects and devices], periodic bremsstrahlung radiators [such as undulator radiation, magnetic bremsstrahlung FEL's (free-electron lasers), and coherent bremsstrahlung in the crystal lattice], and transverse-binding radiators [such as the CRM (cyclotron resonance maser) and channeling radiation]. Starting from a general quantum- electrodynamic model, both quantum and classical effects and operating regimes of these radiation devices are described. The article provides a unified physical description of the interaction kinematics, and presents equations for the characterization of spontaneous and stimulated radiative emission in these various effects and devices. Universal relations between the spontaneous and stimulated emission parameters are revealed and shown to be related (in the quantum limit) to Einstein relations for atomic radiators and (in the classical limit) to the relations derived by Madey for magnetic bremsstrahlung FEL for on-axis radiative emission. Examples for the application of the formulation are given, estimating the feasibility of channeling radiation x-ray laser and optical regime Smith-Purcell FEL, and deriving the gain equations of magnetic bremsstrahlung FEL and CRM for arbitrary electron propagation direction, structure (wiggler) axis, and radiative emission angle.

### 1987

The time-resolved cooperative emission from a system of correlated neutral dissociation fragments, or molecular collision products in beams, is investigated. The investigation is focused on emission at large fragment separations (between 1 nm and a few emission wavelengths), exceeding the domain of short-range interactions within the reactive or collisional molecular complex. A master-equation approach is used to obtain a general expression for the cooperative emission rate, which consists of nonexponential decay factors multiplied by temporal ringing patterns. These features result from the time-dependent radiative coupling between the receding fragments; they depend in an essential manner on the initial electronic state of the parent molecular complex and its symmetry which determine the correlations between the fragments. In the model system of a pair of identical two-level fragments two cases are considered separately. (a) A single photon shared by the fragments, where the emission is initially superradiant or subradiant (radiation trapping), depending on the spin and inversion symmetry of the parent molecular system and of the nascent fragments. The ringing pattern depends on the electronic angular momentum state of the parent molecule and on the polarization of the emitted light. (Such a ringing has been observed recently by Grangier, Aspect, and Vigué [Phys. Rev. Lett. 54, 418 (1985)] in the emission of photodissociated Ca2.) (b) Two initially excited fragments, where the ringing pattern is of smaller amplitude, and is weakly dependent on the electronic angular momentum of the parent molecule. All the aforementioned cooperative features generally last until the fragments recede several radiation wavelengths away from each other. The application of this time-resolved analysis to various diagnostic problems is discussed, especially with regard to the identification of excited electronic states of the parent molecular complex, and the stereospecificity of the fragmental orbitals.

A theory is developed for lasing action from ensembles of relativistically or subrelativistically propagating emitters whose motion is bound in the direction(s) transverse to the direction of propagation. These include relativistic electrons and positrons channeled in crystals or other hollow-channel structures, as well as fast ions wherein a bound electron is perturbed by the crystal potential or laser light. Apart from planar-channeled positrons in crystals, the confining potentials for all other emitters in this category are strongly anharmonic. Therefore, their spectral dipolar transitions are nondegenerate, each involving a different pair of nearly discrete levels of the confining potential. This implies that stimulated emission from such systems can exhibit coherence in the Glauber sense. The theoretical framework presented here consists of Heisenberg equations which have the Maxwell-Bloch form with modifications resulting from the high velocity of the emitters. Steady-state semiclassical solutions of these equations are obtained. It is shown that previous approaches, based on the assumption that the cross section for stimulated emission is uniform throughout the system, do not account for the spatial variation of the polarization at high velocities. As a result, these approaches do not yield the correct gain coefficient whenever the characteristic lengths for the dephasing of the dipole oscillation and for emission amplification are comparable. The latter conditions are realizable in structures composed of channels much wider than in crystals. Lasing schemes are investigated and the prospects for achieving gain in these schemes at wavelengths below 100 A are discussed.