Publications

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.

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.

Our ability to generate new distributions of light has been remarkably enhanced in recent years. At the most fundamental level, these light patterns are obtained by ingeniously combining different electromagnetic modes. Interestingly, the modal superposition occurs in the spatial, temporal as well as spatio-temporal domain. This generalized concept of structured light is being applied across the entire spectrum of optics: generating classical and quantum states of light, harnessing linear and nonlinear light-matter interactions, and advancing applications in microscopy, spectroscopy, holography, communication, and synchronization. This Roadmap highlights the common roots of these different techniques and thus establishes links between research areas that complement each other seamlessly. We provide an overview of all these areas, their backgrounds, current research, and future developments. We highlight the power of multimodal light manipulation and want to inspire new eclectic approaches in this vibrant research community.

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.

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 present efficient fair sampling of ground-state manifold of XY spin Hamiltonian based on dissipatively coupled lasers that includes a massive parallelism. Our simulator could potentially be exploited to address various combinatorial optimization problems.

We demonstrate experimentally and validate theoretically an exact mapping between coupled-lasers networks and classical spin Hamiltonians by adjusting the loss rate of the individual lasers.

The periodicity inherent to any interferometric signal entails a fundamental trade-off between sensitivity and dynamic range of interferometry-based sensors. Here, we develop a methodology for substantially extending the dynamic range of such sensors without compromising their sensitivity, stability, and bandwidth. The scheme is based on simultaneous operation of two nearly identical interferometers, providing a moiré-like period much larger than 2π and benefiting from close-to-maximal sensitivity and from suppression of common-mode noise. The methodology is highly suited to atom interferometers, which offer record sensitivities in measuring gravito-inertial forces but suffer from limited dynamic range. We experimentally demonstrate an atom interferometer with a dynamic-range enhancement of more than an order of magnitude in a single shot and more than three orders of magnitude within a few shots for both static and dynamic signals. This approach can considerably improve the operation of interferometric sensors in challenging, uncertain, or rapidly varying conditions.

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.

The Fresnel-Fizeau effect of transverse drag, in which the trajectory of a light beam changes due to transverse motion of the optical medium, is usually extremely small and hard to detect. We observe transverse drag in a moving hot-vapor cell, utilizing slow light due to electromagnetically induced transparency (EIT). The drag effect is enhanced by a factor 400,000, corresponding to the ratio between the light speed in vacuum and the group velocity under the EIT conditions. We study the contribution of the thermal atomic motion, which is much faster than the mean medium velocity, and identify the regime where its effect on the transverse drag is negligible.

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.

Since the development of laser light sources in the early 1960s, laser beams are everywhere. Laser beams are central in many industrial applications and are essential in ample scientific research fields. Prime scientific examples are optical trapping of ultracold atoms, optical levitation of particles, and laser-based detection of gravitational waves. Mathematically, laser beams are well described by Gaussian beam expressions. Rather well covered in the literature to date are basic expressions for scalar Gaussian beams. In the past, however, higher accuracy mathematics of scalar Gaussian beams and certainly high-accuracy mathematics of vectorial Gaussian beams were far less studied. The objective of the present review then is to summarize and advance the mathematics of vectorial Gaussian beams. When a weakly diverging Gaussian beam, approximated as a linearly polarized two-component plane wave, say (Ex,By), is tightly focused by a high-numerical-aperture lens, the wave is x201C;depolarized.x201D; Namely, the prelens (practically) missing electric field Ey,Ez components suddenly appear. This is similar for the prelens missing Bx,Bz components. In fact, for any divergence angle (x03B8;dlt;1), the ratio of maximum electric field amplitudes of a Gaussian beam Ex:Ez:Ey is roughly 1:x03B8;d2:x03B8;d4. It follows that if a research case involves a tightly focused laser beam, then the case analysis calls for the mathematics of vectorial Gaussian beams. Gaussian-beam-like distributions of the six electricx2013;magnetic vector field components that nearly exactly satisfy Maxwellx2019;s equations are presented. We show that the near-field distributions with and without evanescent waves are markedly different from each other. The here-presented nearly exact six electricx2013;magnetic Gaussian-beam-like field components are symmetric, meaning that the cross-sectional amplitude distribution of Ex(x,y) at any distance (z) is similar to the By(x,y) distribution, Ey(x,y) is similar to Bx(x,y), and a 90x00B0; rotated Ez(x,y) is similar to Bz(x,y). Componentsx2019; symmetry was achieved by executing the steps of an outlined symmetrization procedure. Regardless of how tightly a Gaussian beam is focused, its divergence angle is limited. We show that the full-cone angle to full width at half-maximum intensity of the dominant vector field component does not exceed 60x00B0;. The highest accuracy field distributions to date of the less familiar higher-order Hermitex2013;Gaussian vector components are also presented. Hermitex2013;Gaussian E-B vectors only approximately satisfy Maxwellx2019;s equations. We have defined a Maxwellx2019;s-residual power measure to quantify the approximation quality of different vector sets, and each set approximately (or exactly) satisfies Maxwellx2019;s equations. Several vectorial x201C;applications,x201D; i.e., research fields that involve vector laser beams, are briefly discussed. The mathematics of vectorial Gaussian beams is particularly applicable to the analysis of the physical systems associated with such applications. Two user-friendly x201C;Mathematicax201D; programs, one for computing six high-accuracy vector components of a Hermitex2013;Gaussian beam, and the other for computing the six practically Maxwellx2019;s-equations-satisfying components of a focused laser beam, supplement this review.

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.

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

We present the incorporation of a metasurface involving spin-orbit interaction phenomenon into a laser cavity paving the way for the generation of spin-controlled intra-cavity modes with different topologies.

We use a four-wave mixing process to read-out light from atomic coherence which is continuously written. The light is continuously generated after an effective delay, allowing the atomic coherence to evolve during the process. Contrary to slow-light delay, which depends on the medium optical depth, here the generation delay is determined solely by the intensive properties of the system, approaching the atomic coherence lifetime at the weak driving limit. The atomic evolution during the generation delay is further manifested in the spatial profile of the generated light due to atomic diffusion. Continuous generation of light with a long intrinsic delay can replace discrete write-read procedures when the atomic evolution is the subject of interest.

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.

Talbot diffraction, together with Fourier filtering, are incorporated into a degenerate laser cavity to demonstrate efficient and controlled phase locking of hundreds of coupled lasers formed in different geometries and having different phase distributions. Such a combined approach leads to higher efficiency, better control, and greater variety of output phase distributions than would be possible with either separately. Simulated and experimental results for square, triangular, and honeycomb laser array geometries are presented.

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.

A novel method for converting an array of out-of-phase lasers into one of in-phase lasers that can be tightly focused is presented. The method exploits second-harmonic generation and can be adapted for different laser arrays geometries. Experimental and calculated results, presented for negatively coupled lasers formed in a square, honeycomb, and triangular geometries are in good agreement.

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.

An efficient method to tune the spatial coherence of a degenerate laser over a broad range with minimum variation in the total output power is presented. It is based on varying the diameter of a spatial filter inside the laser cavity. The number of lasing modes supported by the degenerate laser can be controlled from 1 to 320,000, with less than a 50% change in the total output power. We show that a degenerate laser designed for low spatial coherence can be used as an illumination source for speckle-free microscopy that is nine orders of magnitude brighter than conventional thermal light.

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.

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.

Selections from our recent developments in passive phase locking and coherent combining of lasers are presented. These include the principles of our approaches, lasers configurations, experimental procedures and results with solid state lasers and fiber lasers.

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.

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.

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.

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.

Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase, based on the elegant Gaussian modes of optical diffraction. In a light-storage experiment, the complex solutions are imprinted on a gas of diffusing atoms, and the self-similar evolution of both their amplitude and phase pattern is demonstrated. An algebraic decay depending on the mode order is measured. Notably, as opposed to the regular diffusion spreading, a subset of the solutions exhibits a self-similar contraction.

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.

The results of amplifying either radially or azimuthally polarized light with a fiber amplifier are presented. Experimental results reveal that more than 85% polarization purity can be retained at the output even with 40 dB amplification and that efficient conversion of the amplified light to linear polarization can be obtained.

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.

A new compact and robust slab laser configuration which involves passive combining of several laser channels is presented. Light from each laser channel is transferred into the adjacent laser channels by means of a polarizing beam-displacer so as to obtain a combined output with high brightness. In this configuration it is possible to tune the coupling between the laser beams in order to control and optimize the combined output energy. The configuration is experimentally demonstrated by combining five laser channels with high efficiency, and the calculated results are in good agree to experimental results.

A theoretical model characterizing the coherence and phase properties of two weakly coupled lasers is presented. Our calculations show how amplitude dynamics of non-phase locked lasers may enhance coherence by nearly an order of magnitude.

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.

Two coupled fiber laser arrangements demonstrating isochronal and achronal phase locking with long-time-delayed coupling are presented. Experimental results show that stable phase locking with coupling delay lines as long as 4km can be obtained and that phase locking can be invariant to the time delay.

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.

In this paper, we present an approach for passive laser beam combining using plane-parallel intracavity interferometric combiners. With this approach, efficient coherent combining of Gaussian laser beams, transverse single high-order-mode laser beams, and even transverse multimode laser beams is possible. We experimentally obtained a combining efficiency of about 90% when coherently combining 16 solid-state laser channels, as well as when coherently combining four fiber laser channels. We also present an arrangement for simultaneous coherent combining and spectral combining, which could possibly overcome current upscaling limits. We present the basic coherent combining approach, review our past and recent investigations and results with both solid-state and fiber laser configurations, and discuss the possible upscaling and future prospects of this approach.

We study theoretically and experimentally the propagation of slow light in hot atomic vapor and present novel spatial and spectral effects associated with the diffuse atomic motion.

We phase lock an array of 169 Nd:YAG lasers using Fourier filtering in a common degenerated resonator. We observe a wide variety of stable phase structures that are in exact agreement with calculated ones.

We present a scheme for eliminating the optical diffraction of slow light in a thermal atomic medium of electromagnetically induced transparency. Nondiffraction is achieved for an arbitrary paraxial image by manipulating the susceptibility in momentum space, in contrast to the common approach, which employs guidance of specific modes by manipulating the susceptibility in real space. For negative two-photon detuning, the moving atoms drag the transverse momentum components unequally, resulting in a Doppler trapping of light by atoms in two dimensions.

Configurations for efficient free space coherent addition of four separate fiber lasers arranged in two dimensional array are presented. They include compact and robust interferometric combiners that can be inserted either inside or outside the cavity of the combined lasers system. The results reveal that over 85% combining efficiency can be obtained.

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.

We study the effect of thermal atomic motion on slow-light in electromagneticallyinduced transparency medium. By incorporating the atomic motion and collisions into the Maxwell-Bloch equations, we find a spatial-frequency transmission filter that leads to diffusionlike behavior of the slow-light envelope.

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.

We study slowing and storage of three-dimensional light fields in atomic vapor. We demonstrate a technique which reduces the effect of diffusion on the storage fidelity and prove that the phase pattern was also maintained.

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.

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 technique is proposed for generating a tight dark focal spot surrounded by uniform light intensity in all directions. It is based on a single focusing lens illuminated from one side, hence the alignment sensitivities associated with 4π methods are eliminated. Such a beam can be useful, e.g. as a dark atomic trap, and as the erase beam in three dimensional super-resolution fluorescence microscopy.

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 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.

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 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.

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.

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.

A highly efficient intracavity coherent addition of nine individual laser distributions is presented. It is achieved with two passive interferometric combiners that are introduced into the combined laser cavity. The results reveal that the combined output power is greater by almost a factor of 9 compared to that of the single laser distributions, while the beam quality is the same.

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 report on a measurement of splitting in the excitation spectrum of a condensate driven by an optical traveling wave. Experimental results are compared to a numerical solution of the Gross-Pitaevskii equation, and analyzed by a simple two-level model and by the more complete band theory, treating the driving beams as an optical lattice. In this picture, the splitting is a manifestation of the energy gap between neighboring bands that opens on the boundary of the Brillouin zone.

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.

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.

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

The 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.

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.

Efficient coherent addition of nine separate solid state and fiber laser distributions, by means of special interferometric combiners is presented. It is experimentally illustrated with Nd:YAG laser distributions, achieving efficiencies of about 90 percent.

We have discussed the main application areas of diffractive optical elements fabricated on a curved substrate. The versatility of the CDOE comes from the fact that the substrate shape and the grating function can be controlled independently. CDOEs can be used to achieve aberration-free imaging, uniform collimation and ideal concentration of diffuse light at the thermodynamic limit, for general source and target shapes. In high-NA focusing CDOEs can be used to control the effective apodization factor of the focused light rays, and thereby yield uniform and tight focal spots with very low sidelobe intensities. For many applications - like the ideal concentration of diffuse light discussed in Sections 3 and 4, the vectorial diffraction problems mentioned in Section 5, and the optical coordinate transformation described in Section 7 - it is sufficient to optimize the shape of the CDOE, and the grating function can be recorded either holographically with simple spherical or plane waves, or by direct laser lithography. In other cases the grating function must have a more complicated form; here additional optics or computer-generated holograms may be required. Since CDOEs are diffractive elements, they usually have large chromatic aberrations which limit their use to quasi-monochromatic light, except for the spectrograph applications discussed in Section 6. The history of CDOEs began in the mid-19th century with Rowland's curved spectroscopic grating. Thanks to their versatility, and to recent advances in applications, in new design methods, and in holographic recording materials that can be placed on arbitrary shapes and enable high diffraction efficiency, CDOEs should remain a lively area of research in the future too.

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.

The properties of the focal spot for 4π focusing with radially polarized light are presented for various apodization factors. With a focusing system satisfying the Herschel condition, sharp focal spots with almostperfect spherical symmetry (leading to equal axial and transverse resolution) and extremely low sidelobes are achieved.

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

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.

Keywords: FIBER LASERS; QUALITY; POWER

We observe in time-of-flight images a matter-wave fringe pattern for low momentum excitations. The contrast of these fringes is a sensitive spectroscopic probe explained by a Bogoliubov excitation projection and approaches the quantized excitation regime.

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%.

A curved hologram is introduced that allows opportunity to independently control its spatial phase function and its shape. The proper design of the hologram shape yields perfect uniform collimation and concentration of diffuse light at the thermodynamic limit of brightness conservation. The approach of curved holography can be extended to three-dimensional geometry.

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.

This paper presents Bragg spectroscopy of the multi-branch Bogoliubov spectrum of elongated Bose-Einstein condensates. The condensate consists of N=10⁵ atoms of ⁸⁷Rb which was excited at wavenumber k by using two Bragg beams. Results are analyzed by numerically solving the Gross-Pitaevskii (GP) equation for the order parameter of the condensate. This study shows that the response of the condensate to a Bragg pulse is indeed significantly affected by the radial degrees of freedom. By using Bragg pulses longer than in previous measurements, this multi-branch spectrum is resolved, finding good agreement with the predictions of Gross-Pitaevskii theory.

Dark optical traps use repulsive light forces to confine atoms mostly in the dark where their interaction with the trapping light is largely reduced, to enable long coherence times of the trapped atoms combined with tight confinement. We report on single-beam dark optical traps for ultra-cold atoms. These traps were used to demonstrate new spectroscopic and dynamical effects of the trapped atoms, including the observation of regular and chaotic motion in so called optical "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 numerical and experimental investigations to determine the effect of such surface height deviations of the intra-cavity binary phase elements inserted into an Nd-YAG laser and the selection of the Laguerre-Gaussian (0,1) (LG/sub 01/) and Laguerre-Gaussian (0,2) (LG/sub 02/) degenerated modes.

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.

A new type of optical instrument, the curved hologram, is introduced that allows us the unique opportunity to independently control its spatial phase function and its shape (whereas in reflecting or refracting optical elements the shape uniquely determines the spatial phase function). We show how proper design of the hologram shape (using a simple analytic procedure) yields perfect uniform collimation and also collimation and concentration of diffuse (monochromatic) light at the thermodynamic limit of brightness conservation. The results of our experimental demonstration as well as those of our numerical ray-tracing simulations verify our design.

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 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.

The interaction energy of phonons in a Bose-Einstein condensate was directly measured by computerized tomography of TOF images. The measured energy agreed with the predicted Bogoliubov spectrum in the LDA. Hydrodynamic simulations of the release process were consistent with the experimental findings.

We report a measurement of the excitation spectrum omega(k) and the static structure factor S(k) of a Bose-Einstein condensate. The excitation spectrum displays a linear phonon regime, as well as a parabolic single-particle regime. The linear regime provides an upper limit for the super fluid critical velocity, by the Landau criterion. The excitation spectrum agrees well with the Bogoliubov spectrum in the local density approximation, even close to the long-wavelength limit of the region of applicability. Feynman's relation between omega(k) and S(k) is verified, within an overall constant.

As in superfluid ⁴He¹, the excitation spectrum of a Bose-Einstein condensate should give much insight into the system. This paper reports the first measurement of the excitation spectrum, as well as the static structure factor. The excitation spectrum gas been measured by Bragg spectroscopy.

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.

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.

A novel resonator configuration in which it is possible to select two different transverse modes is presented. The intensity distributions of the modes can be chosen to be complementary such that the peaks of the first mode would fall on the valleys of the second mode. Thus, the gain medium can be exploited more efficiently, resulting in an increase in the total output power yet with better beam quality than with the multi-mode operation. A representative resonator configuration, for laser operation with the fundamental TEM₀₀ mode and the Laguerre-Gaussian TEM₀₂ mode is examined.

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.

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.

A scheme to trap atoms in a blue-detuned optical dipole trap, formed with a single laser beam and a holographic phase plate, is demonstrated. 105 rubidium atoms are trapped for (1/e lifetime) ∼300 msec, at temperatures of ∼24 μK. and a density of ∼7 × 10¹¹ atoms/cm³, for a trapping beam detuning of 0.1-30 nm. The time for a trapped atom to scatter one photon off the trapping beam is measured and found to be linear in the trapping laser detuning. At a detuning of 0.5 nm from resonance this time was measured to be ∼100 msec, indicating that the atoms are exposed on average only to ∼1/700 of the maximal light intensity in the trap. The use of a single laser beam allows for simple dynamical changes of the potential and large adiabatic compressions, while keeping the atoms mainly in the dark.

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.

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 diffractive optical system for the transformation of an annular laser beam to a uniform circular beam is presented. It is composed of two diffractive elements which are recorded as surface relief transmission gratings with multilevel discrete binary steps. Our experiments with CO2 laser radiation show that high diffraction efficiencies and good uniformity of the output beam can be achieved.

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.

We present a novel aspheric holographic optical element (HOE), having an extended depth of focus while keeping high lateral resolution. The phase function of the HOE is derived, and computer simulations verify the theoretical prediction for the optical performances.