Publications

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.

The momentum of light in a medium and the mechanisms of momentum transfer between light and dielectrics have long been the topic of controversies and confusion. We discuss here the problem of momentum transfers that follow the refraction of light by dilute, inhomogeneous ensembles of ultra-cold atoms. We show experimentally and theoretically that the refraction of light rays by a dilute gas does not entail momentum transfers to first order in the light-atom coupling coefficient, in contradiction with the work reported in Matzliah et al. Phys. Rev. Lett. 119, 189902 (2017).

We introduce a method to enhance the phase-locking quality and duration of an end-pumped laser array by precisely shaping its pump beam to overlap with the array. Shaping the pump beam results in a significant improvement in lasing efficiency and reduces the pump power required to reach the lasing threshold compared to a typical uniform pumping configuration. Our approach involves shaping a highly incoherent laser beam by addressing smaller segments of the beam with higher local spatial coherence. We demonstrate a remarkable increase in the laser array output brightness by up to a factor of 10, accompanied by a substantial extension in the phase-locking duration.

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.

A many-mode laser with nonlinear modal interaction could serve as a model system to study many-body physics. However, precise and continuous tuning of the interaction strength over a wide range is challenging. Here, we present a unique method for controlling lasing mode structures by introducing random phase fluctuation to a nearly degenerate cavity. We show numerically and experimentally that as the characteristic scale of phase fluctuation decreases by two orders of magnitude, the transverse modes become fragmented and the reduction of their spatial overlap suppresses modal competition for gain, allowing more modes to lase. The tunability, flexibility, and robustness of our system provides a powerful platform for investigating many-body phenomena.

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.

We developed a rapid and efficient method for generating laser outputs with arbitrary shaped distributions and properties that are needed for a variety of applications. It is based on simultaneously controlling the intensity, phase, and coherence distributions of the laser. The method involves a digital degenerate cavity laser in which a phase-only spatial light modulator and spatial filters are incorporated. As a result, a variety of unique and high-resolution arbitrary shaped laser beams were generated with either a low or a high spatial coherence and with a minimal change in the laser output power. By controlling the phase, intensity, and coherence distributions, a shaped laser beam was efficiently reshaped into a completely different shape after free space propagation. The generation of such laser beams could lead to new and interesting applications.

We study the evolution of a BoseEinstein 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 a22 + a11 − 2a12. 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.

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.

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.

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.

We observe a significant steady-state deviation from the generalized equipartition theorem, one of the pivotal results of classical statistical mechanics, in a system of confined, laser-cooled atoms. We parametrize this deviation, measure its dynamics, and show that its steady-state value quantifies the departure of nonthermal states from thermal equilibrium even for anharmonic confinement. In particular, we find that deviations from equipartition grow as the system dynamics becomes more anomalous. We present numerical simulations that validate the experimental data and reveal an inhomogeneous distribution of the kinetic energy through the system, supported by an analytical examination of the phase space.

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.

Tailored physical systems were recently exploited to rapidly solve hard computational challenges, such as spin simulators, combinatorial optimization, and focusing through scattering media. Here, we address the phase retrieval problem where an object is reconstructed from its scattered intensity distribution. This is a key problem in many applications, ranging from x-ray imaging to astrophysics, and currently, it lacks efficient direct reconstruction methods: The widely used indirect iterative algorithms are inherently slow. We present an optical approach based on a digital degenerate cavity laser, whose most probable lasing mode rapidly and efficiently reconstructs the object. Our experimental results suggest that the gain competition between the many lasing modes acts as a highly parallel computer that could rapidly solve the phase retrieval problem. Our approach applies to most two-dimensional objects with known compact support, including complex-valued objects, and can be generalized to imaging through scattering media and other hard computational tasks.

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.

Two approaches for generating flat-top beams (uniform intensity profile) with extended depth of focus are presented. One involves two diffractive optical elements (DOEs) and the other only a single DOE. The results indicate that the depth of focus of such beams strongly depends on the phase distribution at the output of the DOEs. By having uniform phase distribution, it is possible to generate flat-top beams with extended depth of focus. (C) 2018 Optical Society of America

We propose and demonstrate a method to produce a thin and highly collimated annular beam that propagates similarly to an ideal thin Gaussian ring beam, maintaining its excellent propagation properties. Our optical configuration is composed of a binary axicon, a circular binary phase grating, and a lens, making it robust and well suited for high-power lasers. It has a near-perfect circular profile with a dark center, and its large radius to waist ratio is achieved with high conversion efficiency. The measured profile and propagation are in excellent agreement with a numerical Fourier simulation we perform. (C) 2018 Optical Society of America

Novel multi-tasking geometric phase metasurfaces were incorporated into a modified degenerate cavity laser as an output coupler to efficiently generate spin-dependent twisted light beams of different topologies. Multiple harmonic scalar vortex laser beams were formed by replacing the laser output coupler with a shared-aperture metasurface. A variety of distinct wave functions were obtained with an interleaving approach - random interspersing of geometric phase profiles within shared-aperture metasurfaces. Utilizing the interleaved metasurfaces, we generated vectorial vortices by coherently superposing of scalar vortices with opposite topological charges and spin states. We also generated multiple partially coherent vortices by incorporating harmonic response metasurfaces. The incorporation of the metasurface platforms into a laser cavity opens a pathway to novel types of nanophotonic functionalities and enhanced light-matter interactions, offering exciting new opportunities for light manipulation. (c) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

We report the observation of optomechanical strain applied to thermal and quantum degenerate Rb87 atomic clouds when illuminated by an intense, far detuned homogeneous laser beam. In this regime the atomic cloud acts as a lens that focuses the laser beam. As a backaction, the atoms experience a force opposite to the beam deflection, which depends on the atomic cloud density profile. We experimentally demonstrate the basic features of this force, distinguishing it from the well-established scattering and dipole forces. The observed strain saturates, ultimately limiting the momentum impulse that can be transferred to the atoms. This optomechanical force may effectively induce interparticle interactions, which can be optically tuned.

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.

In the past, we investigated degenerate cavity lasers (DCL) which allows manipulation of both near-field and far-field properties of the output beam. The DCL was comprised of a gain medium, two lenses in a 4f telescope configuration, an output coupler at one end and a back mirror at the other end. With the DCL we investigated topological defects in arrays of coupled lasers[1, simulation of classical spins arrays in a frustrated geometry[2, beam focusing after scattering media[3, and lasers with controllable coherence functions for speckles reduction[4. In these investigations, the DCL usually included metallic masks of holes and filters that had to be specifically designed and fabricated for each application.

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 in-phase coupling of hundreds of lasers by means of combined Talbot cavity and intra-cavity spatial Fourier filtering is developed. Simulated and experimental results for square, triangular and honeycomb laser arrays are presented.

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.

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.

Experimental realization for phase-locking large arrays of lasers arranged in a variety of 2D geometries is presented. Using our degenerate-cavity coupling between lasers is easily controlled giving rise to a variety of intriguing phase structures.

For small area beams, the two-photon spectra of atoms diffusing in hot buffer gas approaches a universal, logarithmically-diverging shape, connected to anomalous scale symmetry breaking of a twodimensional Hamiltonian.

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.

We present the phase-locking and coherence properties between two weakly coupled lasers. We show how the degreeofcoherence between the two lasers canbe enhanced bynearly1 order of magnitude after taking into account the effects of coupling on both their phases as well as their amplitudes. Specifically, correlations between synchronized spikes in the amplitude dynamics and the phase dynamics of the lasers allow for an interference pattern with a fringe visibility of 90%, even when the coupling strength is far below the critical value and they are not phase locked.

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.

Phase locking of coupled fiber lasers requires that there exists at least one longitudinal-mode common to all lasers within their bandwidth. As the number of coupled lasers increases, the probability of finding such a longitudinal-mode drops exponentially [1]. Nevertheless, since the length and the corresponding longitudinal-modes of each fiber laser fluctuate randomly due to acoustic and thermal noises, there is a finite probability for having an instantaneous common longitudinal-mode. Due to mode competition, when such a rare event occurs, the lasers lock to this specific longitudinal-mode, resulting in a high fringe visibility interference pattern [2].

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.

A novel configuration for real-time measurement of spacevariant polarizations is presented. The experimental results reveal that the full state of polarization at each location within the beam can be accurately obtained every 10msec, limited only by the detection camera frame rate. We also present a more compact configuration which can be modified to determine the real-time wavelength variant polarization measurements.

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 configurations for phase locking and beam combining very large laser arrays with intra-cavity polarization elements are presented. We demonstrated efficient phase lock of 24 ND:YAG lasers and beam combining of 5 lases.

We present a scheme for eliminating the optical diffraction of images imprinted on slow light in vapor. The elimination of diffraction occurs for arbitrary images all throughout their propagation. An initial experimental demonstration is presented.

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.

In a Bose-Einstein condensate, the excitation of a Bogoliubov phonon with low momentum (e.g., by a two-photon Bragg process) is strongly suppressed due to destructive interference between two indistinguishable excitation pathways. Here we show that scattering of this sound excitation into a double-momentum mode is strongly enhanced due to constructive interference. This enhancement yields an inherent amplification of second-order sound excitations of the condensate, as we confirm experimentally. We further show that due to parity considerations, this effect is extended to higher-order excitations.

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.

A new approach for the simultaneous coherent and spectral addition of a two-dimensional array of fiber lasers is presented. A combining efficiency of over 80% and a combined beam profile with M² = 1.15 were experimentally obtained with an array of four fiber lasers. This approach can lead to significant upscaling in fiber laser additions.

We measure the damping of excitations in cigar-shaped Bose-Einstein condensates of atomic vapor. By using postselection, excitation line shapes of the total population are compared with those of the undamped excitations. We find that the damping depends on the initial excitation energy of the decaying quasiparticle, as well as on the excitation momentum. We model the condensate as an infinite cylinder and calculate the damping rates of the different radial modes. The derived damping rates are in good agreement with the experimentally measured ones. The damping rates strongly depend on the destructive interference between pathways for damping, due to the quantum many-body nature of both excitation and the vacuum modes.

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.

A method for increasing the output energy from newly developed passively Q-switched Englass eyesafe lasers is presented. The increase of energy is achieved by incorporating binary phase elements inside the laser cavities. Experimental results reveal that the output energies can be increased by more than a factor of two. Moreover, by manipulating the output phase with the binary phase elements, the peak energy density in the far field is increased by more than a factor of 4.5.

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.

The Doppler effect is one of the dominant broadening mechanisms in thermal vapor spectroscopy. For two-photon transitions one would naively expect the Doppler effect to cause a residual broadening, proportional to the wave-vector difference. In coherent population trapping (CPT), which is a two-photon narrow-band phenomenon, such broadening was not observed experimentally. This has been commonly attributed to frequent velocity-changing collisions, known to narrow Doppler-broadened one-photon absorption lines (Dicke narrowing). Here we show theoretically that such a narrowing mechanism indeed exists for CPT resonances. The narrowing factor is the ratio between the atom's mean free path and the wavelength associated with the wave-vector difference of the two radiation fields. A possible experiment to verify the theory is suggested.

We develop a round-trip matrix diagonalization method for quantitative description of selection of radially or azimuthally polarized beams by birefringence-induced bifocusing in a simple laser resonator. We employ different focusing between radially and tangentially polarized light in thermally stressed laser rods to obtain low-loss stable oscillation in a radially polarized Laguerre-Gaussian, LG(0, 1)*, mode. We derive a free-space propagator for the radially and azimuthally polarized LG(0, 1)* modes and explain basic principles of mode selection by use of a round-trip matrix diagonalization method. Within this method we calculate round-trip diffraction losses and intensity distributions for the lowest-loss transverse modes. We show that, for the considered laser configuration, the round-trip loss obtained for the radially polarized LG(0, 1)* mode is significantly smaller than that of the azimuthally polarized mode. Our experimental results, obtained with a diode side-pumped Nd:YAG rod in a flat-convex resonator, confirm the theoretical predictions. We achieved a pure radially polarized LG(0, 1)* beam with M² = 2.5 and tens of watts of output power.

An efficient technique in which fiber lasers are coherently added in free space is presented. Since the high power of the combined output light propagates in free space rather than inside, fiber optical damage and deleterious nonlinear effects are substantially reduced. Two different configurations are investigated. One involves conventional intracavity coupling between the lasers. The other is a novel configuration where the coupling is done out of the combined cavities. The latter configuration requires much less coupling for obtaining the same output power, so the damage to the fiber is further reduced.

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.

A unique approach for coherently adding a multiplicity of separate and independent laser distributions with intra-cavity interferometric combiners is developed. The approach which can be scalable is demonstrated with coherent addition of 25 laser distributions.

We quantitatively study the Beliaev decay of Bogoliubov quasi-particles of different energies and momenta in an elongated BEC. The structure of the continuum leads to a momentum dependent collisional shift of the excitation spectrum.

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.

We perform echo spectroscopy on ultracold atoms in atom-optics billiards to study their quantum dynamics. The detuning of the trapping laser is used to change the "perturbation", which causes a decay in the echo coherence. Two different regimes are observed: first, a perturbative regime in which the decay of echo coherence is nonmonotonic and partial revivals of coherence are observed in contrast with the predictions of random matrix theory. These revivals are more pronounced in traps with mixed dynamics as compared to traps where the dynamics is fully chaotic. Next, for stronger perturbations, the decay becomes monotonic and independent of the strength of the perturbation. In this regime no clear distinction can be made between chaotic traps and traps with mixed dynamics.

A dressed-state approach to mixing of bosonic matter waves is presented. Two cases are studied using this formalism. In the first, two macroscopically populated modes of atoms (two-wave mixing) are coupled through the presence of light. In the second case, three modes of Bogoliubov quasiparticles (three-wave mixing) are coupled through s-wave interaction. In both cases, wave mixing induces oscillations in the population of the different modes that decay due to interactions. Analytic expressions for the dressed basis spectrum and the evolution of the mode populations in time are derived both for resonant mixing and nonresonant mixing. Oscillations in the population of a given mode are shown to lead to a splitting in the decay spectrum of that mode, in analogy with the optical Autler-Townes splitting in the decay spectrum of a strongly driven atom. These effects cannot be described by a mean-field approximation.

In this article the design, optimization and characterization of diffractive optical elements formed on a curved surface are reviewed. For such curved diffractive optical elements not only the phase function, but also the surface shape are free parameters that can be used for optimization, yielding much better performances than both flat diffractive optical elements and reflective/refractive optical elements when operating with quasimonochromatic light. We present a new analytic design approach for the surface shape that ensures uniform collimation of a light source with any angular distribution. We demonstrate the usefulness of this design also for ideal (brightness conserving) collimation and concentration of diffuse light, aberration-free imaging, and optical Fourier transform. We present experimental results that confirm our theoretical analysis.

A peak in the static structure factor of a Bose-Einstein condensate is computed, both near and far from a Feshbach resonance. A low-density approximation is made, allowing for an analytic result. A Monte Carlo calculation shows that the peak is larger than predicted by the low-density approximation, for the upper range of densities considered here. The peak could be measured by a probe beam of cold atoms.

An intra-cavity phase clement, combined with a passive Q-switch saturable absorber and a suitable intra-cavity aperture, can provide extremely high mode discrimination, so as to obtain laser operation with single, pure, very high order Laguerre-Gaussian mode. With a Nd:YAG laser setup, well controlled and extremely stable Q-switched operation in the degenerate Laguerre-Gaussian TEM₀₄, TEM₁₄, TEM₂₄, TEM-₃₄, and TEM₄₄ modes was obtained. The measured output energy per pulse for each of these modes was 5.2mJ, 7.5mJ, 10mJ, 12.5mJ, and 13.7mJ respectively, compared to 2.5mJ for the Gaussian mode without the phase element (more than a live fold increase in output energy). Correcting the phase for these modes, so that all transverse lobes have uniform phase, results in a very bright and narrow central lobe in the far field intensity distribution that can theoretically contain more than 90% of the output energy.

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.

Bogoliubov theory for excitations in Bose-Einstein condensates was formulated over 50 years ago to qualitatively explain strongly interacting superfluids. Quantitative experimental verification of this theory came with the long-awaited realization of gaseous, weakly interacting condensates. This Colloquium reviews recent experimental advances in the study of Bogoliubov bulk excitations in Bose-Einstein condensates, obtained using two-photon Bragg scattering.

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.

We show that laser mode stability can be improved with an intracavity mode selecting phase element. Without the phase element, a sub-wavelength change of the distance between the mirrors of a CO₂ laser leads to a substantial change of the transverse mode distribution, whereas with it the distribution remains essentially the same.

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.

The limitations on the coherence time achieved by echo techniques for ultracold atoms trapped in an optical dipole trap were investigated. The improved pulse sequence was demonstrated, for which the decay of coherence was reduced by a factor of 2.5 beyond the reduction offered by the echo spectroscopy. The reduction was found to occur when each dark period in between pulses is shorter that the time scale over which subtantial dephasing develops. It was concluded that the coherence time is limited by mixing to other vibrational levels in the trap and to a lesser extent the lifetime of the internal states of the atoms.

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.

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.

We present a new, compact, and practical optical mode converter that efficiently transforms a high-order Hermite - Gaussian (HG) laser beam into a nearly Gaussian beam. The mode converter is based on coherently adding different transverse parts of the high-order mode beam by use of a single planar interferometric element. The method, configuration, and experimental results obtained with a pulsed Nd:YAG HG TEM₁₀ laser beam are presented. The results reveal that the efficiency of conversion of a HG beam to a nearly Gaussian beam can be as high as 90%.

We investigate the dephasing of ultra cold Rb-85 atoms trapped in an optical dipole trap and prepared in a coherent superposition of their two hyperfine ground states by interaction with a microwave pulse. We demonstrate that the dephasing, measured as the Ramsey fringe contrast, can be reversed by stimulating a coherence echo with a pi pulse between the two pi/2 pulses, in analogy to the photon echo. We also demonstrate that "echo spectroscopy" can be used to study the quantum dynamics in the trap even when more than 10(6) states are thermally populated and to study the crossover from quantum to classical dynamics.

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.

The suppression of inhomogeneous broadening in rf spectroscopy of optically trapped atoms was discussed. A method for reducing the inhomogeneous frequency broadening in the hyperfine splitting of the ground state of optically trapped atoms was presented. The reduction was found to be achieved by the addition of a weak light field spatially mode matched with the trapping field and whose frequency was tuned in between the two hyperfine levels.

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 similar to98%, and the calculated far-field intensity distributions of the output beams are very close to those of corresponding pure LG intensity distributions. The principle of the method, the needed optical arrangement, and calculated and experimental results are presented. (C) 2002 Elsevier Science B.V. All rights reserved.

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 similar to33 times larger than that of existing blue-detuned traps and similar to13 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 similar to1800 times smaller than in a red-detuned trap with the same diameter, depth, and laser power. (C) 2002 Optical Society of America.

We investigate the effects of curving trajectories by applying external force fields on a particle in a billiard. We investigate two special cases: a constant force field and a parabolic potential. These perturbations change the stability conditions and can lead to formation of elliptical orbits in otherwise hyperbolic billiards. We demonstrate these effects experimentally with ultra-cold atoms in atom-optic billiards.

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.

We discuss some properties of dielectric gratings with period comparable with the illuminating wavelength for slanted illumination (this illumination geometry is often referred to as concical mounting). We demonstrate the usefulness of such an illuminating geometry. We show that the threshold period (under which only the zeroth transmission and reflection orders are nonevanescent) can be significantly higher, thereby easing fabrication constraints, and that this illumination setup makes it possible to design achromatic phase retarders. Such a design, for an achromatic quarter-wave plate with λ/60 uniformity of the retardation phase in the 0.470.63μm wavelength interval, is demonstrated.

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 very fast (>100 kHz) acousto-optic scanning system, which relies on two counterpropagating acoustic waves with the same frequency modulation, is proposed and experimentally demonstrated. This scheme completely suppresses linear frequency chirp and thus permits very fast nonlinear scans and nonconstant linear scans. By changing the phase between the modulating signals, this scheme also provides very fast longitudinal scans of the focal point. (C) 2000 Optical Society of America.

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.

Siegman [Opt. Lett. 18, 675 (1993)] showed that binary-phase plates cannot improve laser beam quality. We demonstrate that continuous spiral phase elements can improve the quality of beams that originate from a laser operating with a pure high-order transverse mode. A theoretical analysis is presented, along with experimental results obtained with a CO₂ laser. The results reveal that a nearly optimal Gaussian output beam can be obtained with only a small decrease in the output power.

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 > 10⁶ Rb atoms, and is then compressed adiabatically by a factor of 350 to a final density of 5 × 10¹³ cm^-3. A∼4 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.

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.

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 new approach for optimizing the groove depth of blazed holographic gratings that are illuminated by light with a wide range of wavelengths or incidence angles is presented. The approach is based on choosing the groove depth that maximizes the overall diffraction efficiency over the entire range of incidence angles and wavelengths. The scalar approximation is used for the diffraction efficiency calculations, with some results verified by rigorous vectorial calculations. Analytic solutions are given for some simple examples, together with experimental results.

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 technique for designing holographic optical elements that can perform general types of coordinate transformation is presented. The design is based on analytic ray-tracing techniques for finding the grating vector of the element, from which the holographic grating function is obtained as a solution of a Poissonlike equation. The grating function can be formed either as a computer-generated or as a computer-originated hologram. The design and realization procedure are illustrated for a specific holographic element that performs a logarithmic coordinate transformation on two-dimensional patterns.

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.