Detecting Entanglement from Macroscopic Measurements of the Electric Field and Its Fluctuations.

To address the outstanding task of detecting entanglement in large quantum systems, entanglement witnesses have emerged, addressing the separable nature of a state. Yet optimizing witnesses, or accessing them experimentally, often remains a challenge. We here introduce a family of entanglement witnesses for open quantum systems. Based on the electric field, it does not require state tomography or single-site addressing, but rather macroscopic measurements of the field quadratures and of the total fluorescence. Its efficiency is demonstrated by detecting, from almost any direction, the entanglement of collective single-photon states, such as long-lived states generated by cooperative spontaneous emission. Able to detect entanglement in large open quantum systems, and through a single continuous measurement if operating in the stationary regime, these electric-field-based witnesses can be used on any set of emitters described by the Pauli group, such as atomic systems (cold atoms and trapped ions), giant atoms, color centers, and superconducting qubits.

Laser frequency stabilization by modulation transfer spectroscopy and balanced detection of molecular iodine for laser cooling of 174Yb.

We report laser frequency stabilization by the combination of modulation transfer spectroscopy and balanced detection of a relatively weak hyperfine transition of the R(158)25-0 line of molecular iodine (127I2), which is used as a new frequency reference for laser trapping and cooling of 174Yb on the 1S0 - 3P1 transition. The atomic cloud is characterized by time-of-flight measurements, and an on-resonance optical depth of up to 47 is obtained. We show laser noise reduction and characterize the short-term laser frequency instability by the Allan deviation of the laser fractional frequency. The minimum measured value is 3.9 ×10-13 at 0.17 s of averaging time.

Loading of a large Yb MOT on the 1S0 → 1P1 transition.

We present an experimental setup to laser cool and trap a large number of ytterbium atoms. Our design uses an oven with an array of micro-tubes for efficient collimation of the atomic beam, and we implement a magneto-optical trap of 174Yb on the 1S0 → 1P1 transition at 399 nm. Despite the absence of a Zeeman slower, we obtain a loading of 4 × 109 at./s. We trap up to N = 109 at., where light-assisted collisions become the dominant loss mechanism. We precisely characterize our atomic beam, the loading rate of the magneto-optical trap, and several loss mechanisms relevant for trapping a large number of atoms.

Field and intensity correlations: the Siegert relation from stars to quantum emitters.

The Siegert relation relates field and intensity temporal correlations. After a historical review of the Siegert relation and the Hanbury Brown and Twiss effect, we discuss the validity of this relation in two different domains. We first show that this relation can be used in astrophysics to determine the fundamental parameters of stars, and that it is especially important for the observation with stellar emission lines. Second, we check the validity of this relation for moving quantum scatterers illuminated by a strong driving field.

Lévy flights of photons with infinite mean free path.

Multiple scattering of light by resonant vapor is characterized by Lévy-type superdiffusion with a single-step size distribution p(x)∝1/x^{1+α}. We investigate Lévy flight of light in a hot rubidium vapor collisional-broadened by 50 torr of He gas. The frequent collisions produce Lorentzian absorptive and emissive profiles with α<1 and a corresponding divergent mean step size. We extract the Lévy parameter α≈0.5 in a multiple-scattering regime from radial profile of the transmission and from violation of the Ohm's law. The measured radial transmission profile and the total diffusive transmission curves are well reproduced by numerical simulations for Lorentzian line shapes.

Microscopic and Macroscopic Signatures of 3D Anderson Localization of Light.

Apart from the difficulty of producing highly scattering samples, a major challenge in the observation of Anderson localization of 3D light is identifying an unambiguous signature of the phase transition in experimentally feasible situations. In this Letter, we establish a clear correspondence between the collapse of the conductance, the increase in intensity fluctuations at the localization transition and the scaling analysis results based on the Thouless number, thus connecting the macroscopic and microscopic approaches of localization. Furthermore, the transition thus inferred is fully compatible both with the results based on the eigenvalue analysis of the microscopic description and with the effective-medium Ioffe-Regel criterion.

Nonequilibrium Precondensation of Classical Waves in Two Dimensions Propagating through Atomic Vapors.

The nonlinear Schrödinger equation, used to describe the dynamics of quantum fluids, is known to be valid not only for massive particles but also for the propagation of light in a nonlinear medium, predicting condensation of classical waves. Here we report on the initial evolution of random waves with Gaussian statistics using atomic vapors as an efficient two dimensional nonlinear medium. Experimental and theoretical analysis of near field images reveal a phenomenon of nonequilibrium precondensation, characterized by a fast relaxation towards a precondensate fraction of up to 75%. Such precondensation is in contrast to complete thermalization to the Rayleigh-Jeans equilibrium distribution, requiring prohibitive long interaction lengths.

Matter wave speckle observed in an out-of-equilibrium quantum fluid.

We report the results of the direct comparison of a freely expanding turbulent Bose-Einstein condensate and a propagating optical speckle pattern. We found remarkably similar statistical properties underlying the spatial propagation of both phenomena. The calculated second-order correlation together with the typical correlation length of each system is used to compare and substantiate our observations. We believe that the close analogy existing between an expanding turbulent quantum gas and a traveling optical speckle might burgeon into an exciting research field investigating disordered quantum matter.

Superradiance in a Large and Dilute Cloud of Cold Atoms in the Linear-Optics Regime.

Superradiance has been extensively studied in the 1970s and 1980s in the regime of superfluorescence, where a large number of atoms are initially excited. Cooperative scattering in the linear-optics regime, or "single-photon superradiance," has been investigated much more recently, and superradiant decay has also been predicted, even for a spherical sample of large extent and low density, where the distance between atoms is much larger than the wavelength. Here, we demonstrate this effect experimentally by directly measuring the decay rate of the off-axis fluorescence of a large and dilute cloud of cold rubidium atoms after the sudden switch off of a low-intensity laser driving the atomic transition. We show that, at large detuning, the decay rate increases with the on-resonance optical depth. In contrast to forward scattering, the superradiant decay of off-axis fluorescence is suppressed near resonance due to attenuation and multiple-scattering effects.

Subradiance in a Large Cloud of Cold Atoms.

Since Dicke's seminal paper on coherence in spontaneous radiation by atomic ensembles, superradiance has been extensively studied. Subradiance, on the contrary, has remained elusive, mainly because subradiant states are weakly coupled to the environment and are very sensitive to nonradiative decoherence processes. Here, we report the experimental observation of subradiance in an extended and dilute cold-atom sample containing a large number of particles. We use a far detuned laser to avoid multiple scattering and observe the temporal decay after a sudden switch-off of the laser beam. After the fast decay of most of the fluorescence, we detect a very slow decay, with time constants as long as 100 times the natural lifetime of the excited state of individual atoms. This subradiant time constant scales linearly with the cooperativity parameter, corresponding to the on-resonance optical depth of the sample, and is independent of the laser detuning, as expected from a coupled-dipole model.

QUANTUM SIMULATION. Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins.

Nonequilibrium dynamics of many-body systems are important in many scientific fields. Here, we report the experimental observation of a phase transition of the quantum coherent dynamics of a three-dimensional many-spin system with dipolar interactions. Using nuclear magnetic resonance (NMR) on a solid-state system of spins at room-temperature, we quench the interaction Hamiltonian to drive the evolution of the system. Depending on the quench strength, we then observe either localized or extended dynamics of the system coherence. We extract the critical exponents for the localized cluster size of correlated spins and diffusion coefficient around the phase transition separating the localized from the delocalized dynamical regime. These results show that NMR techniques are well suited to studying the nonequilibrium dynamics of complex many-body systems.

Approximated center-of-mass motion for systems of interacting particles with space- and velocity-dependent friction and anharmonic potential.

We study the center-of-mass motion in systems of trapped interacting particles with space- and velocity-dependent friction and anharmonic traps. Our approach, based on a dynamical ansatz assuming a fixed density profile, allows us to obtain information at once for a wide range of binary interactions and interaction strengths, at linear and nonlinear levels. Our findings are first tested on different simple models by comparison with direct numerical simulations. Then, we apply the method to characterize the motion of the center of mass of a magneto-optical trap and its dependence on the number of trapped atoms. Our predictions are compared with experiments performed on a large Rb(85) magneto-optical trap.

Coherence effects in scattering order expansion of light by atomic clouds.

We interpret cooperative scattering by a collection of cold atoms as a multiple-scattering process. Starting from microscopic equations describing the response of N atoms to a probe light beam, we represent the total scattered field as an infinite series of multiple-scattering events. As an application of the method, we obtain analytical expressions of the coherent intensity in the double-scattering approximation for Gaussian density profiles. In particular, we quantify the contributions of coherent backward and forward scattering.

Controlled Dicke subradiance from a large cloud of two-level systems.

Dicke superradiance has been observed in many systems and is based on constructive interferences between many scattered waves. The counterpart of this enhanced dynamics, subradiance, is a destructive interference effect leading to the partial trapping of light in the system. In contrast to the robust superradiance, subradiant states are fragile, and spurious decoherence phenomena hitherto obstructed the observation of such metastable states. We show that a dilute cloud of cold atoms is an ideal system to look for subradiance in free space and study various mechanisms to control this subradiance.

Threshold of a random laser based on Raman gain in cold atoms.

We address the problem of achieving a random laser with a cloud of cold atoms, in which gain and scattering are provided by the same atoms. In this system, the elastic scattering cross-section is related to the complex atomic polarizability. As a consequence, the random laser threshold is expressed as a function of this polarizability, which can be fully determined by spectroscopic measurements. We apply this idea to experimentally evaluate the threshold of a random laser based on Raman gain between non-degenerate Zeeman states and find a critical optical thickness on the order of 200, which is within reach of state-of-the-art cold-atom experiments.

Threshold of a random laser with cold atoms.

We address the problem of achieving an optical random laser with a cloud of cold atoms, in which gain and scattering are provided by the same atoms. The lasing threshold can be defined using the on-resonance optical thickness b0 as a single critical parameter. We predict the threshold quantitatively, as well as power and frequency of the emitted light, using two different light transport models and the atomic polarizability of a strongly pumped two-level atom. We find a critical b0 on the order of 300, which is within reach of state-of-the-art cold-atom experiments. Interestingly, we find that random lasing can already occur in a regime of relatively low scattering.

Breathing mode for systems of interacting particles.

We study the breathing mode in systems of trapped interacting particles. Our approach, based on a dynamical ansatz in the first equation of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy allows us to tackle at once a wide range of power-law interactions and interaction strengths, at linear and nonlinear levels. This both puts in a common framework various results scattered in the literature, and by widely generalizing these, emphasizes universal characters of this breathing mode. Our findings are supported by direct numerical simulations.

Mechanisms for lasing with cold atoms as the gain medium.

We realize a laser with a cloud of cold rubidium atoms as gain medium, placed in a low-finesse cavity. Three different regimes of laser emission are observed corresponding, respectively, to Mollow, Raman, and four-wave mixing mechanisms. We measure an output power of up to 300 microW and present the main properties of these different lasers in each regime.

Detailed study of an efficient blue laser source by second-harmonic generation in a semimonolithic cavity for the cooling of strontium atoms.

We have constructed a blue laser source consisting of an amplified, grating tuned diode laser that is frequency doubled by a KNbO3 crystal in a compact standing wave cavity and produces as much as 200 mW of internal second-harmonic power. We have analyzed the unusual characteristics of this standing wave cavity to clarify the advantages and disadvantages of this configuration as an alternative to a ring cavity for second-harmonic generation. We emphasize its efficiency and stability and the fact that it has an inherent walk-off compensation, similar to twin crystal configurations. We demonstrate its utility for laser cooling and trapping of earth alkalis by stabilizing the laser to the 461-nm transition of strontium, using a heat pipe, and then forming a magneto-optic trap of strontium from a Zeeman-slowed atomic beam.