Publications

We consider quantum light-matter interfaces comprised of multiple layers of two-dimensional tweezer atomic arrays, wherein the lattice spacings exceed the wavelength of light. While the coupling of light to a single layer of such a "superwavelength"lattice is considerably reduced due to scattering losses to high diffraction orders, we show that the addition of layers can suppress these losses through destructive interference between the layers. Mapping the problem to a 1D model of a quantum interface wherein the coupling efficiency is characterized by a reflectivity, we analyze the latter by developing a geometrical optics formulation, accounting for realistic finite-size arrays. We find that optimized efficiency favors small diffraction-order angles and small interlayer separations, and that the coupling inefficiency for two layers universally scales as N-1 with the atom number per layer N. We validate our predictions using direct numerical calculations of the scattering reflectivity and the performance of a quantum memory protocol, demonstrating high atom-photon coupling efficiency. This opens the way for various applications in tweezer atomic-array platforms.

We consider the coupling of light, via an optical cavity, to two-dimensional atomic arrays whose lattice spacing exceeds the wavelength of the light. Such "superwavelength"spacing is typical of optical tweezer arrays. While subwavelength arrays exhibit strong atom-photon coupling, characterized by high optical reflectivity in free space, the coupling efficiency of superwavelength arrays is reduced due to collective scattering losses to high diffraction orders. We show how a moderate-finesse cavity can overcome these losses. As the scattering losses peak at certain discrete values of the lattice spacing, the spacing can be optimized to achieve efficient atom-photon coupling in the cavity. Our cavity-QED theory properly accounts for collective dipolar interactions mediated by the lossy, non-cavity-confined photon modes and for finite-size effects of both the array and the light field. These findings pave the way to harnessing the versatility of tweezer arrays for efficient atom-photon interfaces in applications of quantum computing, networking, and nonlinear optics.

Finding the global minimum in complex networks while avoiding local minima is challenging in many types of networks. In human networks and communities, adapting and finding new stable states amid changing conditions due to conflicts, climate changes, or disasters, is crucial. We studied the dynamics of complex networks of violin players and observed that such human networks have different methods to avoid local minima than other non-human networks. Humans can change the coupling strength between them or change their tempo. This leads to different dynamics than other networks and makes human networks more robust and better resilient against perturbations. We observed high-order vortex states, oscillation death, and amplitude death, due to the unique dynamics of the network. This research may have implications in politics, economics, pandemic control, decision-making, and predicting the dynamics of networks with artificial intelligence.

We introduce universal, easy-to-reproduce generative models for the QUBO instances to differentiate the performance of the hardware/solvers effectively. Our benchmark process extends the well-known Hebb's rule of associative memory with the asymmetric pattern weights. We provide a comprehensive overview of calculations conducted across various scales and using different classes of dynamical equations. Our aim is to analyze their results, including factors such as the probability of encountering the ground state, planted state, spurious state, or states falling outside the predetermined energy range. Moreover, the generated problems show additional properties, such as the easy-hard-easy complexity transition and complicated cluster structures of planted solutions. Our method establishes a prospective platform to potentially address other questions related to the fundamental principles behind device physics and algorithms for novel computing machines.

Motivated by recent surprising experimental findings, we develop a strong-coupling theory for Bose-Fermi mixtures capable of treating resonant inter-species interactions while satisfying the compressibility sum rule. We show that the mixture can be stable at large interaction strengths close to resonance, in agreement with the experiment but at odds with the widely used perturbation theory. We also calculate the sound velocity of the Bose gas in the 133Cs-6Li mixture, again finding good agreement with the experimental observations both at weak and strong interactions. A central ingredient of our theory is the generalization of a fermion mediated interaction to strong Bose-Fermi scatterings and to finite frequencies. This further leads to a predicted hybridization of the sound modes of the Bose and Fermi gases, which can be directly observed using Bragg spectroscopy.

Diffusion occurs in numerous physical systems throughout nature, drawing its generality from the universality of the central limit theorem. Approximately a century ago it was realized that an extension to this type of dynamics can be obtained in the form of "anomalous"diffusion, where distributions are allowed to have heavy power-law tails. Owing to a unique feature of its momentum-dependent dissipative friction force, laser-cooled atomic ensembles can be used as a test bed for such dynamics. The interplay between laser cooling and anomalous dynamics bears deep predictive implications for fundamental concepts in both equilibrium and nonequilibrium statistical physics. The high degree of control available in cold-atom experiments allows for the parameters of the friction to be tuned, revealing transitions in the dynamical properties of the system. Rare events in both the momentum and spatial distributions are described by non-normalized states using tools adapted from infinite ergodic theory. This leads to new experimental and theoretical results that illuminate the various features of the system.

A moving dielectric medium can displace the optical path of light passing through it, a phenomenon known as the Fresnel-Fizeau optical drag effect. The resulting displacement is proportional to the medium's velocity. In this paper, we report on the observation of an anomalous optical drag effect, where the displacement is still proportional to the medium's speed but along the direction opposite to the medium's movement. We conduct an optical drag experiment under conditions of electromagnetically induced transparency and observe the transition from normal, to null, to anomalous optical drag by modification of the two-photon detuning.

We report on a simple method to reconstruct the band structure of a one-dimensional optical lattice using a thermal cloud with a momentum spread of about two photon recoils. We image the momentum distribution of a thermal cloud exposed to a standing-wave potential using time-of-flight absorption images and observe unique features. With the support of numerical calculations, we explain their appearance and show how they can be used to reconstruct the full band structure directly. While this can serve as a precise lattice depth calibration tool, we additionally propose a method to estimate the lattice depth in a single-shot manner.

The ability to control the chirality of physical devices is of great scientific and technological importance, from investigations of topologically protected edge states in condensed matter systems to wavefront engineering, isolation, and unidirectional communication. When dealing with large networks of oscillators, the control over the chirality of the bulk states becomes significantly more complicated and requires complex apparatus for generating asymmetric coupling or artificial gauge fields. Here we present a new approach for a precise control over the chirality of the bulk state of a triangular array of hundreds of symmetrically coupled lasers, by introducing a weak non-Hermitian complex potential, requiring only local on-site control of loss and frequency. In the unperturbed network, lasing supermodes with opposite chirality (staggered vortex and staggered antivortex) are equally probable. We show that by tuning the complex potential to an exceptional point, a nearly pure chiral lasing supermode is achieved. While our approach is applicable to any oscillators network, we demonstrate how the inherent nonlinearity of the lasers effectively pulls the network to the exceptional point, making the chirality extremely resilient against noise and imperfections.

We introduce a simple, compact two-mirror system for diffuse light concentration. The design principle is based on local conservation of optical brightness. The system design is flexible, and we are able to compute mirror shapes given arbitrary incident beam direction and target cross-sectional shape. As illustration, we showcase our design for flat and cylindrical target geometries, and we also demonstrate that our system is able to concentrate efficiently along one or two dimensions. We perform numeric experiments that confirm our theoretical results and provide diffuse light concentration very close to the thermodynamic limit in all cases we considered.

A unique approach for steady in-phase locking of lasers in an array, regardless of the array geometry, position, orientation, period or size, is presented. The approach relies on the insertion of an intra-cavity Gaussian aperture in the far-field plane of the laser array. Steady in-phase locking of 90 lasers, whose far-field patterns are comprised of sharp spots with extremely high power density, was obtained for various array geometries, even in the presence of near-degenerate solutions, geometric frustration or superimposed independent longitudinal modes. The internal phase structures of the lasers can also be suppressed so as to obtain pure Gaussian mode laser outputs with uniform phase and overall high beam quality. With such phase locking, the laser array can be focused to a sharp spot of high power density, useful for many applications and the research field.

Coupled oscillators such as lasers, optical parametric oscillators, and Bose-Einstein-condensate polaritons can rapidly and efficiently dissipate into a stable phase-locked state that can be mapped onto the minimal energy (ground state) of classical spin Hamiltonians. However, for degenerate or near-degenerate ground-state manifolds, statistical fair sampling is required to obtain complete knowledge of the minimal-energy state, which needs many repetitions of simulations under identical conditions. We show that with dissipatively coupled lasers such fair sampling can be achieved rapidly and accurately by exploiting the many longitudinal modes of each laser to form an ensemble of identical but independent simulators, acting in parallel. We fairly sampled the ground-state manifold of square, triangular, and kagome lattices by measuring their coherence function and identifying manifolds composed of single, doubly degenerate, and highly degenerate ground states, respectively.

Fast speckle suppression is crucial for time-resolved full-field imaging with laser illumination. Here, we introduce a method to accelerate the spatial decoherence of laser emission, achieving speckle suppression in the nanosecond integration time scale. The method relies on the insertion of an intracavity phase diffuser into a degenerate cavity laser to break the frequency degeneracy of transverse modes and broaden the lasing spectrum. The ultrafast decoherence of laser emission results in the reduction of speckle contrast to 3% in less than 1 ns.

We study the evolution of a Bose-Einstein condensate in a two-state superposition due to inter-state interactions. Using a population imbalanced dynamic decoupling scheme, we measure inter-state interactions while canceling intra-state density shifts and external noise sources. Our measurements show low statistical uncertainties for both magnetic sensitive and insensitive superpositions, indicating that we successfully decoupled our system from strong magnetic noises. We experimentally show that the Bloch sphere representing general superposition states is 'twisted' by inter-state interactions, as predicted in [1, 2] and the twist rate depends on the difference between inter-state and intra-state scattering lengths a 22 + a 11-2a 12. We use the non-linear spin dynamics to demonstrate squeezing of Gaussian noise, showing 2.79 0.43 dB squeezing when starting with a noisy state and applying 160 echo pulses, which can be used to increase sensitivity when there are errors in state preparation. Our results allow for a better understanding of inter-Atomic potentials in 87Rb. Our scheme can be used for spin-squeezing beyond the standard quantum limit and observing polaron physics close to Feshbach resonances, where interactions diverge, and strong magnetic noises are ever present.

Fast speckle suppression is crucial for time-resolved full-field imaging with laser illumination. Here, we introduce a method to accelerate the spatial decoherence of laser emission, achieving speckle suppression in the nanosecond integration time scale. The method relies on the insertion of an intracavity phase diffuser into a degenerate cavity laser to break the frequency degeneracy of transverse modes and broaden the lasing spectrum. The ultrafast decoherence of laser emission results in the reduction of speckle contrast to 3% in less than 1 ns.

Synchronization of different and independent oscillators that interact with each other via a common intermediate is ubiquitous in many fields. Here, we experimentally demonstrate the effect of crowd synchrony, analogous to that of the Millennium Bridge, by resorting to coupled lasers. When the number of lasers is below a critical number, there is no synchronization, but after reaching the critical number, the lasers instantaneously synchronize. We show that the synchronization of the lasers as a function of their number follows a first-order transition, and that our experimental results are in good agreement with those predicted by theoretical models.

Quantum measurement remains a puzzle through its stormy history from the birth of quantum mechanics to state-of-the-art quantum technologies. Two complementary measurement schemes have been widely investigated in a variety of quantum systems: von Neumanns projective strong measurement and Aharonovs weak measurement. Here, we report the observation of a weak-to-strong measurement transition in a single trapped ⁴⁰Ca⁺ ion system. The transition is realized by tuning the interaction strength between the ions internal electronic state and its vibrational motion, which play the roles of the measured system and the measuring pointer, respectively. By pre- and post-selecting the internal state, a pointer state composed of two of the ions motional wavepackets is obtained, and its central-position shift, which corresponds to the measurement outcome, demonstrates the transition from the weak-value asymptotes to the expectation-value asymptotes. Quantitatively, the weak-to-strong measurement transition is characterized by a universal transition factor e−Γ2/2, where Γ is a dimensionless parameter related to the systemapparatus coupling. This transition, which continuously connects weak measurements and strong measurements, may open new experimental possibilities to test quantum foundations and prompt us to re-examine and improve the measurement schemes of related quantum technologies.

Point-source atom interferometry is a promising approach for implementing robust, high-sensitivity, rotation sensors using cold atoms. However, its scale factor, i.e., the ratio between the interferometer signal and the actual rotation rate, depends on the initial conditions of the atomic cloud, which may drift in time and result in bias instability, particularly in compact devices with short interrogation times. We present two methods to stabilize the scale factor. One relies on a model-based correction which exploits correlations between multiple features of the interferometer output and works on a single-shot basis. The other is a self-calibrating method where a known bias rotation is applied to every other measurement, requiring no prior knowledge of the underlying model but reducing the sensor bandwidth by a factor of two. We demonstrate both schemes experimentally with complete suppression of scale-factor drifts, maintaining the original rotation sensitivity and allowing for bias-free operation over several hours.

Coupled oscillators such as lasers, optical parametric oscillators, and Bose-Einstein-condensate polaritons can rapidly and efficiently dissipate into a stable phase-locked state that can be mapped onto the minimal energy (ground state) of classical spin Hamiltonians. However, for degenerate or near-degenerate ground-state manifolds, statistical fair sampling is required to obtain complete knowledge of the minimal-energy state, which needs many repetitions of simulations under identical conditions. We show that with dissipatively coupled lasers such fair sampling can be achieved rapidly and accurately by exploiting the many longitudinal modes of each laser to form an ensemble of identical but independent simulators, acting in parallel. We fairly sampled the ground-state manifold of square, triangular, and kagome lattices by measuring their coherence function and identifying manifolds composed of single, doubly degenerate, and highly degenerate ground states, respectively.

Atom interferometers offer excellent sensitivity to gravitational and inertial signals but have limited dynamic range. We introduce a scheme that improves this trade-off by a factor of 50 using composite fringes, obtained from sets of measurements with slightly varying interrogation times, as in a moire effect. We analyze analytically the performance gain in this approach and the trade-offs it entails between sensitivity, dynamic range, and bandwidth, and we experimentally validate the analysis over a wide range of parameters. Combining composite-fringe measurements with a particle-filter estimation protocol, we demonstrate continuous tracking of a rapidly varying signal over a span 2 orders of magnitude larger than the dynamic range of a traditional atom interferometer.

Interactions in an ultracold boson-fermion mixture are often manifested by elastic collisions. In a mixture of a condensed Bose gas (BEC) and spin polarized degenerate Fermi gas (DFG), fermions can mediate spin-spin interactions between bosons, leading to an effective long-range magnetic interaction analogous to Ruderman-Kittcl-Kasuya-Yosida [Phys. Rev. 96, 99 (1954); Prog. Theor. Phys. 16, 45 (1956); Phys. Rev. 106, 893 (1957)] interaction in solids. We used Ramsey spectroscopy of the hyperfine clock transition in a Rb-87 BEC to measure the interaction mediated by a K-40 DFG. By controlling the boson density we isolated the effect of mediated interactions from mean-field frequency shifts due to direct collision with fermions. We measured an increase of boson spin-spin interaction by a factor of eta = 1.45 +/- 0.05(stat) +/- 0.13(syst) in the presence of the DFG, providing clear evidence of spin-spin fennion mediated interaction. Decoherence in our system was dominated by inhomogeneous boson density shift, which increased significantly in the presence of the DFG, again indicating mediated interactions. We also measured a frequency shift due to boson-fermion interactions in accordance with a scattering length difference of a(bf2) - a(bf1) = -5.36 +/- 0.44(stat) +/- 1.43(syst)a(0) between the clock-transition states, a first measurement beyond the low-energy elastic approximation [R. Cote, & A. Dalgarno, H. Wang, and W. C. Stwalley, Phys. Rev. A 57, R4118 (1998); A. Dalgarno and M. Rudge, Proc. R. Soc. A 286, 519 (1965)] in this mixture. This interaction can be tuned with a future use of a boson-fermion Feshbach resonance. Fermion-mediated interactions can potentially give rise to interesting new magnetic phases and extend the Bose-Hubbard model when the atoms are placed in an optical lattice.

Designs based on single diffractive-optical-elements for obtaining flat-top laser intensity distributions that remain constant over a long range during free-space propagation are presented. Flat-top beams with different orders n exhibit a different range of propagation. For various working distances z, the resulting flat-top beam yields a different depth of focus. By controlling spectral properties of laser distributions, it is possible to maintain invariant flat-top intensity distributions for relatively long propagation distances.

The dynamics of topological defects in a system of coupled phase oscillators, arranged in one and two-dimensional arrays, was numerically investigated using the Kuramoto model. After a rapid decay of the number of topological defects, a long-time quasi steady state with few topological defects was detected. Two competing time scales governed the dynamics corresponding to the dissipation rate and the coupling quench rate. The density of topological defects scales as a power law function of the coupling quench rate rho similar to C-nu with nu = 0.25. Reducing the number of topological defects improves the long time coherence and order parameter of the system, enhancing the probability to reach a global minimal loss state that can be mapped to the ground state of a classical XY spin Hamiltonian.

We present techniques for inertial-sensing atom interferometers which produce multiple phase measurements per experimental cycle. With these techniques, we realize two types of multiport measurements, namely, quadrature phase detection and real-time systematic phase cancellation, which address challenges in operating high-sensitivity cold-atom sensors in mobile and field applications. We confirm experimentally the increase in sensitivity due to quadrature phase detection in the presence of large phase uncertainty, and demonstrate suppression of systematic phases on a single-shot basis.

Lasers have enabled scientific and technological progress, owing to their high brightness and high coherence. However, the high spatial coherence of laser illumination is not always desirable, because it can cause adverse artefacts such as speckle noise. To reduce spatial coherence, new laser cavity geometries and alternative feedback mechanisms have been developed. By tailoring the spatial and spectral properties of cavity resonances, the number of lasing modes, the emission profiles and the coherence properties can be controlled. In this Technical Review, we present an overview of such unconventional, complex lasers, with a focus on their spatial coherence properties. Laser coherence control not only provides an efficient means for eliminating coherent artefacts but also enables new applications in imaging and wavefront shaping. High spatial coherence of laser illumination is not always desirable, because it can cause adverse artefacts such as speckle noise. This Technical Review describes unconventional lasers that have inherently low and/or tunable spatial coherence. Key pointsHigh spatial coherence of laser emission, a common feature of conventional lasers, causes deleterious effects, including speckle noise and crosstalk, in applications such as full-field imaging, display, materials processing, photolithography, holography and optical trapping.Fundamental changes in laser design or operation are more effective than schemes to reduce the spatial coherence outside of the laser cavity to achieve low or tunable spatial coherence.Random lasers and wave-chaotic microcavity lasers support numerous lasing modes with distinct spatial profiles, producing emission of low spatial coherence suitable for speckle-free, full-field imaging and spatial coherence gating.The number of modes and thus spatial coherence of degenerate cavity laser emission can be tuned with little change in power, allowing fast switching between speckle-free imaging and speckle-contrast imaging.Wavefront shaping inside a degenerate cavity laser can generate propagation-invariant output beams or spin-dependent twisted light beams. The dynamic wavefront control can focus laser light through a random scattering medium.

Loading an ultra-cold ensemble into a static magnetic trap involves unavoidable loss of phase space density when the gravitational energy dominates the kinetic energy of the ensemble. In such a case the gravitational energy is transformed into heat, making a subsequent evaporation process slower and less efficient. We apply a high phase space loading scheme on a sub-doppler cooled ensemble of Rubidium atoms, with a gravitational energy much higher than its temperature of . Using the regular configuration of a quadrupole magnetic trap, but driving unequal currents through the coils to allow the trap center to fall, we dissipate most of the gravitational energy and obtain a 20-fold improvement in the phase space density as compared to optimal loading into a static magnetic trap. Applying this scheme, we start an efficient and fast evaporation process as a result of the sub-second thermalization rate of the magnetically trapped ensemble.

Spatial coherence quantifies spatial field correlations and is one of the fundamental properties of light. Here we investigate the spatial coherence of highly multimode lasers in the regime of short timescales. Counterintuitively, we show that in this regime, the temporal (longitudinal) modes play a crucial role in spatial coherence reduction. To evaluate the spatial coherence we measured the temporal dynamics of speckle fields generated by a highly multimode laser with over 10(5) lasing spatial (transverse) modes and examined the dependence of speckle contrast on the exposure time of the detecting device. We show that in the regime of short timescales, the spatial and temporal modes interact to form spatiotemporal supermodes, such that the spatial degrees of freedom are encoded onto the temporal modes. As a result, the speckle contrast is suppressed according to the number of temporal modes, and the degree of spatial coherence is reduced. Moreover, the functional form of the spatial coherence is shown to have a bimodal distribution. In the regime of long timescales, the supermodes are no longer a valid representation of the laser modal structure. Consequently, the spatial coherence is independent of the temporal modes, and the classical result, where the speckle contrast is suppressed according to the number of spatial modes, is obtained. Due to this spatiotemporal mechanism, highly multimode lasers can be used for speckle suppression in high-speed full-field imaging applications, as we demonstrate here for imaging of a fast moving object.

Incorporation of a metasurface that involves spin-orbit interaction phenomenon into a laser cavity provides a route to the generation of spin-controlled intracavity modes with different topologies. By utilizing the geometric phase, Pancharatnam-Berry phase, we found a spin-enabled self-consistent cavity solution of a Nd:YAG laser with a silicon-based metasurface. Using this solution we generated a laser mode possessing spin-controlled orbital-angular momentum. Moreover, an experimental demonstration of a vectorial vortex is achieved by the coherent superposition of modes with opposite spin and orbital angular momenta. We experimentally achieved a high mode purity of 95% due to laser mode competition and purification. The photonic spin-orbit interaction mechanism within a laser-cavity can be implemented with multifunctional shared aperture nanoantenna arrays to achieve multiple intracavity topologies.

A rapid and efficient all-optical method for forming propagation invariant shaped beams by exploiting the optical feedback of a laser cavity is presented. The method is based on the modified degenerate cavity laser (MDCL), which is a highly incoherent cavity laser. The MDCL has a very large number of degrees of freedom (320,000 modes in our system) that can be coupled and controlled, and allows direct access to both the real space and Fourier space of the laser beam. By inserting amplitude masks into the cavity, constraints can be imposed on the laser in order to obtain minimal loss solutions that would optimally lead to a superposition of Bessel-Gauss beams forming a desired shaped beam. The resulting beam maintains its transverse intensity distribution for relatively long propagation distances. (c) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.

We perform Raman spectroscopy of optically trapped noninteracting Rb87 atoms, and observe revivals of the atomic coherence at integer multiples of the trap period. The effect of coherence control methods such as echo and dynamical decoupling is investigated experimentally, analytically, and numerically, along with the effect of the anharmonicity of the trapping potential. The latter is shown to be responsible for incompleteness of the revivals. Coherent Raman control of trapped atoms can be useful in the context of free-oscillation atom interferometry and spatial multimode quantum memory.

The softness of elastic atomic collisions, defined as the average number of collisions each atom undergoes until its energy decorrelates significantly, can have a considerable effect on the decay dynamics of atomic coherence. In this paper we combine two spectroscopic methods to measure these dynamics and obtain the collisional softness of ultracold atoms in an optical trap: Ramsey spectroscopy to measure the energy decorrelation rate and echo spectroscopy to measure the collision rate. We obtain a value of 2.5(3) for the collisional softness, in good agreement with previously reported numerical molecular-dynamics simulations. This fundamental quantity is used to determine the s-wave scattering lengths of different atoms but has not been directly measured. We further show that the decay dynamics of the revival amplitudes in the echo experiment has a transition in its functional decay. The transition time is related to the softness of the collisions and provides yet another way to approximate it. These conclusions are supported by Monte Carlo simulations of the full echo dynamics. The methods presented here can allow measurement of a generalized softness parameter for other two-level quantum systems with discrete spectral fluctuations.

In this Letter, we present a measurement of the phase-space density distribution (PSDD) of ultracold Rb-87 atoms performing 1D anomalous diffusion. The PSDD is imaged using a direct tomographic method based on Raman velocity selection. It reveals that the position-velocity correlation function C-xv(t) builds up on a time scale related to the initial conditions of the ensemble and then decays asymptotically as a power law. We show that the decay follows a simple scaling theory involving the power-law asymptotic dynamics of position and velocity. The generality of this scaling theory is confirmed using Monte Carlo simulations of two distinct models of anomalous diffusion.

This paper describes a technique that allows measurement of very small alternating accelerations. It is based on a quantum version of a lock-in amplifier, 1 which filters out spectral components far from the frequency of the measured signal, improving the signal-to-noise ratio of the measurement. As a proof-of-principle, a controlled experiment using microwave radiation is performed, modulating the phase of the control pulses at a given frequency. A strong response at twice the modulation frequency is observed as expected. Preliminary results of measurements taken with Raman control are also presented, in which a controlled modulation of the phase was obtained by modulating a piezoelectric actuator, causing one of the Raman mirrors to vibrate.

Control of the propagation properties of complex beams is desired for many applications. Here we present a novel method to generate propagation invariant shaped beams. Our method is based on a modified degenerate cavity (MDC) [1], [2], which has a huge number of degrees of freedom (300,000 modes in our system), that can be coupled and controlled. Specifically, the MDC allows direct access to both the x-space and k-space components of the laser beam. Accordingly, placing two amplitude masks, one in x-space and one in k-space, enables control of the output beam. Varying the geometric properties of the mask in x-space changes the shape of the output beam, and varying the geometric properties of the mask in k-space breaks the degeneracy between modes and forms spatial correlations (partial spatial coherence) in the output beam [1].

Talbot diffraction coupling is exploited for controlling phase locking and demonstrating topological charge effects in laser arrays formed in a degenerate cavity. Experimental and calculated results for different array geometries are demonstrated.

Second harmonic generation in coupled laser arrays is exploited to convert out-of-phase lasers into in-phase lasers and reveal hitherto unknown properties of some laser array geometries.

Efficient method for manipulating the spatial coherence of a laser is presented. Different mutual intensity coherence functions, such as cosine or Bessel functions, are obtained, and number of modes is controlled in 1D and 2D.

The effects of topological charge on phase locking an array of coupled lasers are presented. This is done with even and odd number of lasers arranged on a ring geometry. With an even number of lasers the topological-charge effect is negligible, whereas with an odd number of lasers the topological-charge effect is clearly detected. Experimental and calculated results show how the topological charge effects degrade the quality of the phase locking, and how they can be removed. Our results shed further light on the frustration and also the quality of phase locking of coupled laser arrays.

We propose and investigate theoretically a new concept for single-large-mode amplification in double-clad active fibers. The concept is based on exploiting a very small fiber core, guiding only a single transverse mode that has large overlap with a doped active cladding. We show that the guided mode can have very large area with good modal discrimination. This simple structured fiber can be used in an 'all-fiber' configuration. We further investigate the sensitivity to small refractive index changes of the doped area and to bending of the fiber. Our proposed fiber concept could lead to fibers with very large mode area with advantages over current commercial fibers.

The synchronization of chaotic lasers and the optical phase synchronization of light originating in multiple coupled lasers have both been extensively studied. However, the interplay between these two phenomena, especially at the network level, is unexplored. Here, we experimentally compare these phenomena by controlling the heterogeneity of the coupling delay times of two lasers. While chaotic lasers exhibit deterioration in synchronization as the time delay heterogeneity increases, phase synchronization is found to be independent of heterogeneity. The experimental results are found to be in agreement with numerical simulations for semiconductor lasers.

Coherent diffusion pertains to the motion of atomic dipoles experiencing frequent collisions in vapor while maintaining their coherence. Recent theoretical and experimental studies on the effect of coherent diffusion on key Raman processes, namely, Raman spectroscopy, slow polariton propagation, and stored light, are reviewed in this Colloquium.

We measure the statistics of phase locking levels of coupled fiber lasers with fluctuating cavity lengths. We found that the measured distribution of the phase locking level of such coupled lasers can be described by the generalized extreme value distribution. For large number of lasers the distribution of the phase locking level can be approximated by a Gumbel distribution. We present a simple model, based on the spectral response of coupled lasers, and the calculated results are in good agreement with the experimental results.

The dynamics of modes and their states of polarizations in multimode fibers as a function of time, space, and wavelength are experimentally and theoretically investigated. The results reveal that the states of polarizations are displaced in Poincaré sphere representation when varying the angular orientations of the polarization at the incident light. Such displacements, which complicate the interpretation of the results, are overcome by resorting to modified Poincaré sphere representation. With such modification it should be possible to predict the output modes and their state of polarization when the input mode and state of polarization are known.

We determined the probability distribution of the combined output power from 25 coupled fiber lasers and show that it agrees well with the Tracy-Widom and Majumdar-Vergassola distributions of the largest eigenvalue of Wishart random matrices with no fitting parameters. This was achieved with 500 000 measurements of the combined output power from the fiber lasers, that continuously changes with variations of the fiber lasers lengths. We show experimentally that for small deviations of the combined output power over its mean value the Tracy-Widom distribution is correct, while for large deviations the Majumdar-Vergassola distribution is correct.

We present a direct measurement of the bath coupling spectrum in an ensemble of trapped ultracold atoms, by applying a spectrally narrow-band control field. From the inferred spectrum, we predict the performance of some dynamical decoupling sequences.

A new concept for focusing light through a randomly disordered media is demonstrated. Results show how by placing the randomly scattering media directly into a laser cavity tight focusing is accomplished in less than 600ns.

We experimentally investigate the phase dynamics of laser networks with homogenous time-delayed mutual coupling and establish the fundamental rules that govern their state of synchronization. We identified a specific substructure that imposes its synchronization state on the entire network and show that for any coupling configuration the network forms at most two synchronized clusters. Our results indicate that the synchronization state of the network is a nonlocal phenomenon and cannot be deduced by decomposing the network into smaller substructures, each with its individual synchronization state.

A compact configuration for real-time achromatic measurements of space-variant light polarization is presented. The experimental results reveal that the full state of polarization at each location within a light beam or at each wavelength can be obtained with accuracy of over π /18.

The dynamics of the state of polarization in multimode fiber amplifiers is presented. The experimental results reveal that although the state of polarizations at the output can vary over a large range when changing the temperatures of the fiber amplifiers, the variations are significantly reduced when resorting to the principal states of polarization in single-mode fiber amplifiers and principal modes in multimode fiber amplifiers.

Experimental results on the interplay between the topology of time-delayed coupled laser networks and their phase synchronization are presented. These establish the fundamental rules that govern the synchronization state of the entire network.

Experimental realization for phase locking several thousands of lasers arranged in a variety of 2D geometries is presented. Coupling ranges and sign are easily controlled giving rise to a variety of intriguing phase structures.

Experimental realization for phase locking several thousands of lasers arranged in a variety of 2D geometries is presented. Coupling ranges and sign are easily controlled giving rise to a variety of intriguing phase structures.

A novel configuration for amplifying radial or azimuthal polarized light with fiber amplifier is presented. We obtained 40dB amplification with more than 85% polarization purity and efficient conversion to linear polarization.

Slow-light polaritons in a thermal vapor experience abnormal diffraction when detuned from a pump laser. Diffraction manipulation is demonstrated for a uniform pump, and a Schrödinger-like dynamics with induced vector-potential is demonstrated for structured pumps.

We study the spectral narrowing induced by collisions in a dense cold atomic ensemble. We report on experiments showing a prolongation of the coherence time of optically trapped Rb87 atoms as the density increases, a phenomenon we call collisional narrowing in analogy to the motional narrowing effect in NMR. We derive an expression for the new dephasing time scale in terms of the collision rate and the inhomogeneous decay time. Remarkably, this time scale universally depends only on the atomic phase space density.

We study, theoretically and experimentally, an ensemble of two-level systems coupled to an environment which induces random jumps in their resonant frequency. We present a closed-form formula for the spectrum in terms of the resonant frequency distribution and the Poisson rate constant. For a normal distribution the spectrum deviates from a generalized Gumbel function, a well-known result for continuous stochastic Gaussian processes. We perform experiments with optically trapped cold Rb87 atoms and show that the predictions of our theory for a 3D harmonic trap match the measured spectra without fitting parameters.

Our experiments on passively phase locking two-dimensional arrays of coupled fiber lasers reveal that the average phase locking level of 25 lasers is low (20%-30%) but can exceed 90% in rare brief events. The average phase locking level was found to decrease for a larger number of lasers in the array and to increase with the connectivity of the array.

Detailed experimental and theoretical investigations of two coupled fiber lasers, each with many longitudinal modes, reveal that the behavior of the longitudinal modes depends on both the coupling strength and the detuning between them. For low to moderate coupling strength only longitudinal modes that are common for both lasers phase lock, while those that are not common gradually disappear. For larger coupling strengths, the longitudinal modes that are not common reappear and phase lock. When the coupling strength approaches unity the coupled lasers behave as a single long cavity with correspondingly denser longitudinal modes. Finally, we show that the gradual increase in phase locking as a function of the coupling strength results from competition between phase-locked and non-phase-locked longitudinal modes.

We study the coherence dynamics of optically trapped ⁸⁷Rb atoms. We observe a decrease of the dephasing rate for an increasing elastic collision rate, and show that it depends only on the phase space density.

We employ dynamical decoupling techniques to suppress the decoherence induced by elastic collisions in optically trapped ⁸⁷Rb atoms. Coherence times exceeding 3 sec in a dense ensemble are demonstrated for an arbitrary initial state.

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.

We experimentally demonstrate electromagnetically induced transparency and light storage with ultracold Rb87 atoms in a Mott insulating state in a three-dimensional optical lattice. We have observed light storage times of 240ms, to our knowledge the longest ever achieved in ultracold atomic samples. Using the differential light shift caused by a spatially inhomogeneous far detuned light field we imprint a "phase gradient" across the atomic sample, resulting in controlled angular redirection of the retrieved light pulse.

We report the observation of the signature of a localization phase transition for light in one-dimensional quasiperiodic photonic lattices, by directly measuring wave transport inside the lattice. Below the predicted transition point an initially narrow wave packet expands as it propagates, while above the transition expansion is fully suppressed. In addition, we measure the effect of focusing nonlinear interaction on the propagation and find it increases the width of the localized wave packets.

We report an experiment that directly measures the Laplace transform of the recurrence probability in one dimension using electromagnetically induced transparency (EIT) of coherent atoms diffusing in a vapor cell filled with buffer gas. We find a regime where the limiting form of the complex EIT spectrum is universal and only depends on the effective dimensionality in which the random recurrence takes place. In an effective one-dimensional diffusion setting, the measured spectrum exhibits power-law dependence over two decades in the frequency domain with a critical exponent of 0.56 close to the expected value 0.5.

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.

New con-gurations for phase locking and beam combining very large laser arrays with intra-cavity polarization elements are presented. We demonstrated e±cient phase lock of 24 ND:YAG lasers and beam combining of 5 lases.

Two-photon processes that involve different sublevels of the ground state of an atom, are highly sensitive to depopulation and decoherence within the ground state. For example, the spectral width of electromagnetically induced transparency resonances in a Λ -type system, are strongly affected by the ground-state depopulation and decoherence rates. We present a direct measurement of decay rates between hyperfine and Zeeman sublevels in the ground state of Rb87 vapor. Similar to the relaxation-in-the-dark technique, pumping lasers are used to prealign the atomic vapor in a well-defined quantum state. The free propagation of the atomic state is monitored using a Ramsey-like method. Coherence times in the range 1-10 ms were measured for room temperature atomic vapor. In the range of the experimental parameters used in this study, the dominant process inducing Zeeman decoherence is the spin-exchange collisions between rubidium atoms.

New configurations for phase locking several laser beams with intracavity polarization elements are presented. With this configuration we demonstrated efficient phase lock of up to 24 ND:YAG laser beams with only two polarization beam displacers.

Efficient free-space configurations for phase locking and coherent addition of two fiber lasers, each operating with a high-order mode, are presented. Experimental results reveal that when the two fiber lasers are coupled, the polarization and modal distribution of one are imposed on the other. Coherent addition with a combining efficiency larger than 90% was achieved.

Radially-polarized beams can be strongly amplified without significant birefringence-induced aberrations. However, further improvement of the beam quality and beam brightness is desirable. We demonstrate two new efficient methods for transformation of the radially-polarized Laguerre-Gaussian beam to a nearly-Gaussian beam with much higher beam quality. The methods are based on separation the radially-polarized mode into two degenerate modes and their coherent addition after the phase flattening. We present detailed analysis and compare the two methods. With one of the methods, we transformed a high-power radially-polarized (0, 1)^* Laguerre-Gaussian beam with M² = 2.52 and power of 30 W, to a nearly-Gaussian beam with M² = 1.3. As a result, the laser beam brightness increased by a factor of ∼2.5.

We present results on phase-locking dynamics of coupled lasers near threshold, and their dependence on spontaneous emission. Our experimental and analytical results clearly reveal that phase locking depends strongly on quantum noise when the coupled lasers oscillate near threshold.

Reversible and coherent storage of light in an atomic medium is a promising method with possible applications in many fields. In this work, arbitrary two-dimensional images are slowed and stored in warm atomic vapor for up to 30μs, utilizing electromagnetically induced transparency. Both the intensity and the phase patterns of the optical field are maintained. The main limitation on the storage resolution and duration is found to be the diffusion of atoms. A technique analogous to phase-shift lithography is employed to diminish the effect of diffusion on the visibility of the reconstructed image.

We present a theoretical model for electromagnetically induced transparency (EIT) in vapor that incorporates atomic motion and velocity-changing collisions into the dynamics of the density-matrix distribution. Within a unified formalism, we demonstrate various motional effects, known for EIT in vapor: Doppler broadening of the absorption spectrum; Dicke narrowing and time-of-flight broadening of the transmission window for a finite-sized probe; diffusion of atomic coherence during storage of light and diffusion of the light-matter excitation during slow-light propagation; and Ramsey narrowing of the spectrum for a probe and pump beams of finite size.

Phase locking, which is achieved by transferring some energy from one oscillator to the others, strongly depends on the coupling strength between the oscillators. Typically, the coupling strength must be above a certain threshold in order to achieve phase locking. Here we show how this threshold can be significantly reduced when phase-dependent losses are introduced into the oscillators. Specifically, the coupling strength can be reduced by at least an order of magnitude, thereby substantially decreasing the needed transfer of energy between oscillators. The resulting enhancement of phase locking does not only influence the laser research area, but also affects many other areas that involve coupled ensembles.

A simple, robust, and efficient method to produce either radially or azimuthally polarized output beam from a fiber laser is presented. Experimental results reveal that polarization purity of 90% or better can be obtained.

A new type of diffractive optical element for detecting and measuring the power distribution of transverse modes emanating from radially symmetric laser resonators is presented. It is based on a relatively simple straightforward design of a phase-only diffractive optical element that serves as a matched filter, which correlates between specific prerecorded transverse modes with a certain azimuthal mode order and those in the incident laser light. Computer simulations supported by experimental results demonstrate how such elements can accurately detect modes with spiral phases and provide quantitative results on the modal power distribution.

We study experimentally superradiance in a Bose-Einstein condensate using a two-frequency pump beam. By controlling the frequency difference between the beam components, we measure the spectrum of the backward (energy-mismatched) superradiant atomic modes. In addition, we show that the populations of these modes display coherent time dynamics. These results are compared to a semiclassical model based on coupled Schrödinger-Maxwell equations.

Dicke narrowing is a phenomenon that dramatically reduces the Doppler width of spectral lines, due to frequent velocity-changing collisions. A similar phenomenon occurs for electromagnetically induced transparency (EIT) resonances, and facilitates ultranarrow spectral features in room-temperature vapor. We directly measure the Dicke-like narrowing by studying EIT line shapes as a function of the angle between the pump and probe beams. The measurements are in good agreement with an analytic theory with no fit parameters. The results show that Dicke narrowing can increase substantially the tolerance of hot-vapor EIT to angular deviations. We demonstrate the importance of this effect for applications such as imaging and spatial solitons using a single-shot imaging experiment, and discuss the implications for the feasibility of storing images in atomic vapor.

Rapidly oscillating potentials with a vanishing time average have been used for a long time to trap charged particles in source-free regions. It has been argued that the motion of a particle inside such a potential can be approximately described by a time independent effective potential, which does not depend upon the initial phase of the oscillating potential. However, here we show that the motion of a particle and its trapping condition significantly depend upon this initial phase for arbitrarily high frequencies of the potential's oscillation. We explain this phenomenon by showing that the motion of a particle is determined by the effective potential stated in the literature only if its initial conditions are transformed according to a transformation which we show to significantly depend on the potential's initial phase for arbitrarily high frequencies. We confirm our theoretical findings by numerical simulations. Further, we demonstrate that the found phenomenon offers different ways to manipulate the dynamics of particles which are trapped by rapidly oscillating potentials. Finally, we propose a simple experiment to verify the theoretical findings of this work.

We report an experiment in which an optical vortex is stored in a vapor of Rb atoms. Because of its 2π phase twist, this mode, also known as the Laguerre-Gauss mode, is topologically stable and cannot unwind even under conditions of strong diffusion. For comparison, we stored a Gaussian beam with a dark center and a uniform phase. Contrary to the optical vortex, which stays stable for over 100μs, the dark center in the retrieved flat-phased image was filled with light after a storage time as short as 10μs. The experiment proves that higher electromagnetic modes can be converted into atomic coherences and that modes with phase singularities are robust to decoherence effects such as diffusion. This opens the possibility to more elaborate schemes for classical and quantum information storage in atomic vapors.

The dependence of fluorescence depletion on the relative polarizations of pump and erase beams is investigated for a sample of randomly oriented Rhodamine-6G molecules. The significance of polarization effects is illustrated for two existing systems of fluorescence depletion super-resolution microscopy: a circular polarization setup, and an azimuth-linear polarization setup.

The properties of tight dark focal spot created using a simple circular π phase plate are presented. For focusing elements with low numerical aperture, the focal plane intensity has r⁴ dependence, while for focusing elements with high numerical aperture, vectorial diffraction effects become important, and the focal plane intensity surprisingly approaches r² dependence, indicating a much tighter dark spot.

Loschmidt echo of atoms trapped in atom optics billiards with chaotic and mixed dynamics is realized by performing a microwave Ramsey sequence to their internal state.

By releasing ultra-cold atoms from a small red detuned Gaussian trap to an optical wedge billiard we reduce the energy broadening of the atoms and perform spatial selection on the initial occupied phase space.

The efficient intracavity coherent addition of 16 separate laser Gaussian mode distributions is presented. The coherent addition is achieved in a multichannel pulsed Nd:YAG laser resonator by use of four intracavity interferometric beam combiners. The results reveal 88% combining efficiency with a combined output beam of nearly pure Gaussian distribution.

"Zero-mean" optical potentials are used to manipulate dephasing of ultra-cold atoms confined in atom-optical billiards. Generic and non-generic perturbations result in qualitatively different dephasing properties. Different phase-space regimes are probed and identified.

The properties of the focal spot for 4π focusing with radially polarized first-order Laguerre - Gaussian beams are calculated. It is shown that a focal spot that has an extremely sharp dark region at the center and an almost-perfect spherical symmetry can be achieved. When such a hollow dark spherical spot is used in 4π fluorescence depletion microscopy, an axial FWHM spot size of ∼39 nm and a transverse FWHM spot size of ∼64 nm can be achieved simultaneously in a practical system.

We study the collisional decay of a strongly driven Bose-Einstein condensate oscillating between two momentum modes. The resulting products of the decay are found to strongly deviate from the usual s-wave halo. Using a stochastically seeded classical field method we simulate the collisional manifold. These results are also explained by a model of colliding Bloch states.

We perform spectroscopy on the ground-state hyperfine splitting of ⁸⁵Rb atoms trapped in far-off-resonance optical traps. The existence of a spatially dependent shift in the energy levels is shown to induce an inherent dephasing effect, which causes a broadening of the spectroscopic line and hence an inhomogeneous loss of atomic coherence at a much faster rate than the homogeneous one caused by spontaneous photon scattering. We present here a number of approaches for reducing this inhomogeneous broadening, based on trap geometry, additional laser fields, and novel microwave pulse sequences. We then show how hyperfine spectroscopy can be used to study the quantum dynamics of optically trapped atoms.

We report on efficient intracavity coherent addition of several single high-order mode distributions in a multichannel laser resonator. The phase locking and coherent addition is achieved by using an intracavity interferometric beam combiner. The principle, configuration, and experimental results with pulsed Nd:YAG Laguerre-Gaussian TEM₀₁ and TEM ₀₂ laser beam distributions are presented. The results reveal more than 95% combining efficiency with a nearly pure high-order mode output beam distribution in both free-running and Q-switched operation.

Intracavity coherent addition of several laser channel distributions where one is a Gaussian distribution and the others are multimode distributions is investigated. It is shown experimentally that the Gaussian distribution is inherently imposed on all the channels. A model for analyzing coherent addition of two or four beams is developed and used to support the experimental results.

Multimode laser operation is usually characterized by high output power, yet its beam quality is inferior to that of a laser with single TEM₀₀ mode operation. Here we present an efficient approach for improving the beam quality of multimode laser resonators. The approach is based on splitting the intra-cavity multimode beam into an array of smaller beams, each with a high quality beam distribution, which are coherently added within the resonator. The coupling between the beams in the array and their coherent addition is achieved with planar interferometric beam combiners. Experimental verification, where the intra-cavity multimode beam in a pulsed Nd:YAG laser resonator is split into four Gaussian beams that are then coherently added, provides a total increase in brightness of one order of magnitude. Additional spectral measurements indicate that scaling to larger coherent arrays is possible.

We developed a new experimental system (the "atom-optics billiard") and demonstrated chaotic and regular dynamics of cold, optically trapped atoms. We show that the softness of the walls and additional optical potentials can be used to manipulate the structure of phase space.

The onset of superfluidity in random media has been extensively studied with quantum He⁴ fluids. The recent observation of superfluid to Mott-insulator quantum phase transition in an ultra cold dilute Bose gas, presents a new prospect for studying such phenomena in a well controlled environment [1]. In particular, by introducing disorder in a controlled manner, new phases of matter are expected to form. Here we focus on the effect of hopping disorder on the onset of superfluidity of a BEC immersed in a deep and disordered optical lattice, where the use of the Bose-Hubbard Hamiltonian is justified. We introduce disorder via a bond percolation model by weakening each nearest-neighbor tunneling element with a probability p. We formulate and solve a renormalization-group equation to find the critical percolation threshold P_c and the accompanying critical exponent v [2]. We check different values for the strength of the weakened bond ranging from the Mott-insulator regime to the superfluid regime and find that there is a critical value under which the superfluid response will greatly diminish (see figure 1). We also analyze a mean field version of the same problem, and an exact ID model and indicate possible experiments that may support our results.

Very high-order transverse mode selection using intra-cavity phase elements in passive Q-switched Nd:YAG and Er:glass lasers is reported. Stable operation of pure high-order modes is achieved(TEM₄₄), resulting in considerable increase of output powers.

We report on efficient coherent addition of spatially incoherent multimode laser beam distributions. Such addition is demonstrated within a multi-channel laser resonator configuration, obtaining more than 90% combining efficiency while preserving the good beam quality. We explain the rather surprising physical phenomenon of coherently adding spatially incoherent light by self-phase-locking of each of the modal components within the multimode beams. Our approach could lead to significantly higher output powers concomitantly with good beam qualities than were hitherto possible in laser systems.

A compact and practical combined laser resonator configuration, with several Gaussian beam distributions combined efficiently, was analyzed. Resonator was based on interactive coherent addition of pairs of Gaussian beam distributions with a planar interferometric coupler. The resonator was designed for coherent combining of Gaussian beam field distributions but could be extended by pairing of two Gaussian beams. The results show that the resonator possess 92% combining efficiency with nearly Gaussian output beam.

A series of measurements of decoherence and wave-packet dephasing between two colliding, strongly coupled, identical Bose-Einstein condensates was reported. A suppression of the mean-field shift was measured in the strong-excitation regime. The suppression was explained by applying the Gross-Pitaevskii energy functional. The oscillations for which both inhomogeneous and Doppler broadening were strongly suppressed were observed by selectively counting only the nondecohered fraction in a time-of-flight image. It was observed that collisions can be extracted if no post-selection is used.

Recently, Dorn et al. [Phys. Rev. Lett. 91, 233901 (2003)] demonstrated the significance of radially polarized doughnut beams in obtaining very small focal spots (with an area of ~0.26λ²) with high-numerical-aperture (NA) aplanatic microscope objectives. We propose two simple alternative ways to focus such radially polarized beams: a parabolic mirror and a f lat diffractive lens. Because of their large apodization factor for a high NA, a significant further reduction in spot area (up to a factor of 1.76 at a NA of 1) compared with the aplanatic system can be achieved.

We present an approach for efficient conversion of a single-high-order-mode distribution from a laser to a nearly Gaussian distribution and vice versa. It is based on dividing the high-order mode distribution into equal parts that are then combined together coherently. We implement our approach with several optical arrangements that include a combination of discrete elements and some with single interferometric elements. These arrangements are analyzed and experimentally evaluated for converting the TEM₀₁ mode distribution with M_x² = 3 to a nearly Gaussian beam with M_x² = 1.045 or M_x² = 1.15. The basic principle, design, and experimental results obtained with several conversion arrangements are presented. The results reveal that conversion efficiency is typically greater than 90%, compared with theoretical ones. In addition, some arrangement is exploited for converting the fundamental Gaussian-beam distribution into the TEM₀₁ mode distribution.

A new type of diffractive optical instrument, the curved hologram, for which the spatial phase function and the hologram shape can be controlled independently, is investigated for finite distance concentration of diffuse (quasi-monochromatic) light. We show how a simple analytic design for given light source and target geometries yields spatially uniform concentrations of diffuse light at the thermodynamic limit of brightness conservation. Such diffractive elements may provide a useful alternative to reflective cavities for efficient and uniform side-pumping of solid-state lasers.

We present numerical and experimental results for the development of islands of stability in atom-optics billiards with soft walls. As the walls are soften, stable regions appear near singular periodic trajectories in converging (focusing) and dispersing billiards, and are surrounded by areas of "stickiness" in phase space. The size of these islands depends on the softness of the potential in a very sensitive way.

Reflective light-guiding tubes having chaotic and integrable cross-sectional shapes are investigated. The applicability of chaotic billiard shapes as cross-sections versus integrable ones for specific beam shaping purposes is demonstrated. Three important cases are considered: homogenizing, anamorphic collimation and concentration of diffuse light.

A dressed basis is used to calculate the dynamics of three-wave mixing between Bogoliubov quasiparticles in a Bose condensate. Because of the observed oscillations between different momentum modes, an energy splitting, analogous to the optical Mollow triplet, appears in the Beliaev damping spectrum of the excitations from the oscillating modes.

Long Bragg pulses were used to spectroscopically measure the first and zeroth order radial modes in the phonon spectrum of a Bose-Einstein condensate. These high-resolution measurements agree well with simulations of the Gross-Pitaevskii equation. The local density approximation failed to reproduce these multiple radial modes.

A macroscopic coherence, lost as a consequence of dephasing of the different populated motional levels was efficiently revived by stimulating an echo if the trap detunings is large enough so ||≃1. This suppression of dephasing due to perturbations induced by the trap yielded a dramatic increase in the coherence time for trapped atoms that may find important applications for precision spectroscopy and quantum information processing.

The principles and experimental results of a new compact optical mode converter that efficiently transforms (above 90 percent efficiency) a high order Hermite-Gaussian laser beam into a nearly Gaussian beam are presented.

Several methods for operating a laser with a single high-order transverse mode are presented. These methods are based on the insertion of binary and spiral phase elements within the laser resonator, so as to introduce high losses to the undesired modes and low losses to the desired mode, as well as controlling the phases of the various lobes of the high order mode distribution. The basic principles and experimental results are presented, demonstrating efficient high order mode selection in various Nd:YAG and CO/sub 2/ laser configurations, where the far-field intensity distribution is comprised mainly of a dominant main lobe. The experiments were performed with low gain CW lasers as well as short-pulse-high-gain Q-switched lasers.

In this paper, we present a relatively simple and practical approach for efficiently conversing of a single high-order mode intensity distribution to a nearly Gaussian distribution. It is based on dividing the high-order mode distribution into equal parts that are then combined together coherently. Experimentally we implement this approach with single interferometric elements, whose surfaces are specially coated. With single interferometric element, the interferometric stability is significantly improved and the complexity of alignment is reduced.

This work investigates the dephasing of ultra cold ⁸⁵Rb atoms trapped in an optical dipole trap and prepared in a coherent superposition of the two hyperfine ground states by interaction with a so-called π/2 micro wave (MW) pulse. The dephasing, measured as the Ramsey fringe contrast decay and related with the Loschmidt echo decay, can be reversed by stimulating a "coherence echo". The later is obtained by adding a population-inverting "p" pulse between the usual two π/2 pulses. Echo spectroscopy on atoms in a Gaussian beam red-detuned trap is performed and observed, for the proper trap parameters, a coherent signal, which for long times decays due to photon scattering, and has a time scale two orders of magnitude longer than the Ramsey decoherence times.

A method for reducing the inhomogeneous broadening in the spectroscopic measurement of the hyperfine splitting of the ground state of optically trapped atoms is demonstrated. This reduction is achieved by the addition of a very weak light field (the "compensating beam"), whose frequency is tuned between the two hyperfine levels. The total shift is obtained by adding the shifts from the trap and the compensating beam, and a complete cancellation of the inhomogeneous broadening will occur for an intensity ratio of ∼ (ΔHF/2δ)². With the suppression of inhomogeneous broadening, the atomic coherence time is next limited by the much smaller spontaneous scattering time. Finally, the introduction of the compensating beam provides with an experimental method to control the decoherence rate of the atomic ensemble, and thus to study the interesting interplay between dynamics and coherence in systems with a rich phase-space, for example in atom-optics billiards.

A simple method for obtaining a nearly Gaussian laser beam from a high order Hermite-Gaussian mode is presented. The method is based on separating the equal lobes of the high order mode and combining them together coherently. The method was experimentally verified with an arrangement of three mirrors, a 50% beam splitter and a phase tuning plate. The beam quality factor calculated in x-direction for the resulting output beam is 1.045, being very close to that of ideal Gaussian beam. The calculated power leakage is only 1.5 %. The experimental near-field and far-field intensity distributions of the output beam have nearly Gaussian cross sections in both the x and the y directions, with M²_x=1.34 and M²_y=32. With some modifications, it is possible to obtain an output beam with M²_x=1.15 and no power leakage.

We present a method for reducing the inhomogeneous frequency broadening
in the hyperfine splitting of the ground state of optically trapped
atoms. This reduction is achieved by the addition of a weak light field,
spatially mode matched with the trapping field and whose frequency is
tuned in between the two hyperfine levels. We experimentally demonstrate
the new scheme with 85Rb atoms, and report a 50-fold narrowing of the rf spectrum.

A method for efficiently converting a Gaussian beam into a helical Laguerre-Gaussian (LG) beam is presented. It is based on using a pair of axicons to produce a shifted-Gaussian (doughnut) intensity distribution that is then passed through a spiral phase element. It is shown that the conversion efficiency can be as high as

We propose a new scheme for constructing a single-beam dark optical trap that minimizes light-induced perturbations of the trapped atoms. The proposed scheme optimizes the trap depth for given trapping laser power and detuning by creating a light envelope with (a) an almost minimal surface area for a given volume and (b) the minimal wall thickness that is allowed by diffraction. The stiffness of the trap's walls, combined with the large detuning allowed by the efficient distribution of light intensity, yields a low spontaneous photon scattering rate for the trapped atoms. Our trap also optimizes the loading efficiency by maximizing the geometrical overlap between a magneto-optical trap and the dipole trap. We demonstrate this new scheme by generating the proposed light distribution of a single-beam dark trap with a trap depth that is ∼33 times larger than that of existing blue-detuned traps and ∼13 times larger than that of a red-detuned trap with the same diameter, detuning, and laser power. Trapped atoms are predicted to have a decoherence rate that is >200 times smaller than in existing single-beam dark traps and -1800 times smaller than in a red-detuned trap with the same diameter, depth, and laser power.

A measurement of the static structure factor S(k) and the excitation spectrum ω(k) of a Bose-Einstein condensate (BEC), was presented. The excitation spectrum consisted of a linear phonon regime, as well as a single-particle regime and the linear regime provided an upper limit for the superfluid critical velocity, by the Landau criterion. The results showed that the excitation spectrum agreed quantitatively with the Bogoliubov spectrum, in the local density approximation.

Classical dynamics of curved-trajectory billiards that would be hyperbolic if the particle had moved in straight lines were investigated. As such, the curvature by applying external force fields on the particle was introduced. It was analytically shown that this can lead to the formation of elliptical orbits in hyperbolic billiards, and experimentally demonstrate these effects, using atom-optics billiards where ultra-cold atoms were trapped inside a dark optical trap, whose shape can be varied to create different atom dynamics.

The relation between the energy and the momentum of the excitation is given by the Bogoliubov dispersion relation. Thus, both the momentum and energy of the excited BEC cloud are measured by performing tomographic analysis on time-of-flight (TOF) images of the excited atoms. It is found that the atoms that carry the momentum of the excitation out of the BEC cloud, carry the entire excitation energy.

Aplanatic curved diffractive element for imaging and light concentration were discussed. Interference pattern of two ordinary spherical or plane waves on a spherical surface was recorded. It was found that a diffractive optical element (DOE) that fulfills the Abbe sine condition suppresses all first-order (monochromatic) aberrations.

We demonstrate an imaging diffractive optical element (DOE) that is free of coma and other first-order aberrations. The DOE was holographically recorded on a properly curved surface and thereby satisfies the Abbe sine (aplanatic) condition. Experimental results as well as numerical ray-tracing simulations indicate that the off-axis aberrations of the curved DOE are much smaller than those of a flat DOE. Because the recording of the DOE involves a single step and only readily available spherical and plane waves, it is extremely simple.

We propose and experimentally demonstrate an acousto-optic cylindrical lens with a very fast (400-kHz) focal scanning. The lens is realized by use of two adjacent acousto-optic scanners with counterpropagating acoustic waves that have the same frequency modulation but a π phase difference. This scheme completely suppresses the lateral scan but adds the linear chirp of the two waves and thus functions as a fast focal-scan lens. We also demonstrate the use of this scanning lens in a very fast confocal profilometer.

A technique for diffuse beam shaping is presented. The beam shaping is achieved by a single reflection on an element, which consists of many displaced parallel planar reflecting facets. The reflecting facets approximate a designed curved surface. We demonstrate the validity of the method for the conversion of a diffuse Gaussian beam into a uniform one in one of the spatial dimensions.

A novel configuration for concentrating diffuse, based on a reflective curved diffractive element, is proposed and demonstrated. Such an aplanatic element satisfies the Abbe sine condition, and hence can achieve diffuse light concentration close to the thermodynamic limit. In our experiments, a thin, cylindrically shaped diffractive element with a numerical aperture of 0.86 yielded a one-dimensional concentration ratio that was 80% of the thermodynamic limit.

Summary form only given. The motion of a particle inside a closed area surrounded by reflecting walls can be integrable or chaotic, depending on the shape of the boundary. These billiards serve as a good and simple model to study chaotic dynamics both classically and quantum mechanically. Recently, we realized an "atom-optics billiard", where ultra-cold atoms are trapped inside a dark optical trap, whose shape can be varied to create different atom dynamics. In this work we describe how scattering and wall softness influence the dynamics of the atoms, and destroy or create stability.

We describe frequency locking of a diode laser to a two-photon transition of rubidium using the Zeeman modulation technique. We locked and tuned the laser frequency by modulating and shifting the twophoton transition frequency with ac and dc magnetic fields. We achieved a linewidth of 500 kHz and continuous tunability over 280 MHz with no laser frequency modulation.

A novel method for forming pure helical laser beams of pre-determined helicity is presented. It is mainly based on replacing one of the laser mirrors with a spiral phase element. The basic principles along with experimental results using a CO₂ laser are described.

A novel method to trap ultracold atoms in a single-beam, dark optical dipole trap, which uses a binary phase element, is proposed and demonstrated. The length and the width of this trap are independently controlled to enable a larger volume, a more symmetric shape, and a higher loading efficiency. More than 10⁶ rubidium atoms were loaded into the trap at a trapping laser detuning of 0.1-10 nm above the atomic transition.

We propose a new spectroscopic method for measuring weak transitions in cold and trapped atoms, which exploits the long spin relaxation times and tight spatial confinement offered by dark optical traps to achieve extremely high sensitivity. We demonstrate our scheme by measuring a 5S_1/2 → 5D_5/2 two-photon transition in cold Rb atoms trapped in a new single-beam dark optical trap, using an extremely weak probe laser power of 25 μW. We were able to measure transitions with as small excitation rate as -1, using 10⁷ fold quantum amplification of the transition rate due to spin shelving and normalized detection with a strong cycling transition. * Present address: Institute of Applied Physics, Technical University of Sofia, 1780 Sofia, Bulgaria.

We propose and demonstrate a scheme for a blue-detuned optical dipole trap for cold atoms which consists of a single, rapidly rotating laser beam. We characterize a parameter range in which the optical potential can be accurately described by a quasistatic time-averaged potential. The trap is loaded with [Formula Presented] Rb atoms, and is then compressed adiabatically by a factor of 350 to a final density of [Formula Presented] [Formula Presented] [Formula Presented] times adiabatic increase in the peak phase-space density of the trapped atoms is obtained due to the change in the shape of the trap potential. The two-body elastic and inelastic collision rates of atoms in the compressed trap are determined.

Three new atom-optics applications based on rapidly scanning beams have been reported. These applications included (1) the generation of different types of dynamics for atoms confined by a (time-averaged) optical potential; (2) the generation of nearly parabolic two-dimensional potentials by rotating a Gaussian beam with a radius R = 0.55W₀ (where W₀ is its 1/e - radius); and (3) the demonstration of an output coupler for a circularly polarized scanning-beam optical trap.

A new and extremely sensitive method for measuring weak transitions with cold atoms in a dark optical trap is presented. The scheme is realized on a 5S _1/2 → 5D_5/2 two-photon transition in cold and optically trapped ₈₅Rb atoms.

The performance of high numerical aperture (NA) focusing lenses to focus light into small spot, leading to high resolution and concentration of light was investigated. Vectorial formulation was applied to the diffractive lenses for calculating the polarization effects and apodization factor. Intensity distributions at the focal plane as a function of NA gave the spot size according to either width of central lobe or 84 percent of the focused energy.

A novel method for discriminating and selecting a specific high order mode is presented. It is based on introducing spiral phase elements into a laser resonator, so as to improve the output beam quality over that when the laser operates with multi-modes, and yet maintain a relatively high output power. The theoretical analysis, along with experimental results with CO₂ and Nd:YAG lasers are presented. The results reveal that a 50% increase of laser output power over that operating with TEM₀₀ mode is possible.

We analyze the light-induced atom-atom interactions in optically thick atomic clouds and show that, when the laser frequency is on-resonance with the atomic transition, they become attractive. On the basis of this analysis we propose and demonstrate a novel scheme to compress a cold and dense atomic cloud with a short onresonance laser pulse. The compression force arises from attenuation of the laser light by the atomic cloud. The following free propagation of the atoms shows a lenslike behavior that yields a transient density increase at the focal time, where neither laser nor magnetic field perturbations exist. A cooling pulse, which is applied at the focal time of this lens, restores the initial temperature of atoms, and hence the phase space density is increased. Finally, we adopt our compression scheme to a quasi-steady-state mode by temporally chopping it with the cooling and trapping beams of a magnet-optical trap.

Discontinuous phase elements can be inserted into laser resonators so that the lasers will operate with only one desired high order transverse mode. These elements introduce sharp discontinuous phase changes so as to result in minimal losses for a desired transverse mode but high losses to others. The basic principles, along with experimental results with Nd:yttrium-aluminum-garnet and CO₂ lasers, illustrating improved output powers with a high beam quality of low divergence, are presented.

We propose and demonstrate a new scheme to fabricate surface relief binary phase elements by using selective deposition of dielectric layers through a contact mask. By using in situ optical thickness monitoring, accurate (∼1%), repeatable, and robust layer thicknesses are readily obtained, leading to accurate phases. We demonstrate our scheme by forming a circular π phase element that is used to form a dark optical trap for atoms.

A novel configuration of a single-beam blue-detuned optical dipole trap based on rapidly rotating laser beam is presented. Large dynamical changes of the potential size and shape were readily obtained due to the simplicity of the trap. A large initial volume provided an efficient loading into the trap and an adiabatic decrease of the trap size yielded a dramatic increase in the atomic density. It was verified that trap stability occurs for rotation frequency higher than the oscillation atomic frequency in the time-average potential.

An approach is presented for anamorphic concentration of diffuse light to achieve extremely high concentration in one lateral direction at the expense of the other direction. The approach is based on free-space optics and involves two arrays of prisms, or holographic optical elements that perform the necessary coupling between the two spatial directions.

The density capabilities of free-space optical interconnects are analyzed by applying Gabors theory of information. It is shown that it is possible to increase the space-bandwidth product capabilities of space-variant interconnect schemes if they have symmetry properties. Several examples of such symmetries (locality, separability and smoothness) are discussed in detail, together with some experimen¬tal results.

A novel method for designing and recording aspheric computer generated holographic optical elements for far infrared radiation has been developed. The design method is based on analytic ray-tracing procedure that exploits the minimization of the mean-squared difference of the propagation vectors between the actual output wavefronts and the desired output wavefronts. This minimization yields a solution for the aspheric grating vector. The design method is illustrated by recording and testing aspheric reflective and transmissive off-axis focussing elements for 10.6 μm wavelength having diffraction-limited performance over a broad range of incidence angles.

A technique for forming nondiffracting beams having essentially constant intensity along the propagation direction is presented. In this technique two phase-only holographic elements are exploited to form the nondiffractive beam as well as to obtain a high diffraction efficiency. The elements were designed and formed as computer generated holograms, and the combination was tested experimentally, showing a good agreement with the predicted behavior.

A novel single multifunctional holographic optical element is incorporated into a surface measurement system. As a result the system is lightweight, compact, and simpler than conventional ones. Numerical calculation reveals that submicron resolutions are possible both in the horizontal and vertical directions. Finally, experimental results demonstrate the feasibility of the approach.

A new method for performing optical coordinate transformation is presented. It is based on a curved holographic element on which the interference pattern of two perpendicular plane waves is recorded. The design procedures and results for two curved elements that perform a one-dimensional logarithmic coordinate transformation and a Gaussian-to-uniform-beam conversion are given.

We report a novel aspheric holographic optical element, the holographic axilens, for achieving extended focal depth while keeping high lateral resolution. The element is designed according to special optimization techniques and recorded as a computer-generated hologram. The results for a specific element, which has a depth of focus of 30 mm, a lateral resolution of 80 μm, a focal length of 1250 mm, and a diameter of 12.5 mm at a wavelength of 633 nm, are presented.