Abstract:
Multiple scattering is a process in which a particle is repeatedly deflected by other particles. In an overwhelming majority of cases, the ensuing random walk can successfully be described through Gaussian, or normal, statistics. However, like a (growing) number of other apparently inofensive systems, diffusion of light in dilute atomic vapours eludes this familiar interpretation, exhibiting a superdiffusive behavior. As opposed to normal diffusion, whereby the particle executes steps in random directions but with lengths slightly varying around an average value (like a drunkard whose next move is unpredictable but certain to within a few tens of centimeters), superdiffusion is characterized by sudden abnormally long steps (L\'{e}vy flights) interrupting sequences of apparently regular jumps which, although very rare, determine the whole dynamics of the system. The formal statistics tools to describe superdiffusion already exist and rely on stable, well understood distributions. As scientists become aware of, and more familiar with, this non-orthodox possibility of interpretation of random phenomena, new systems are discovered or re-interpreted as following L\'{e}vy statistics. Propagation of light in resonant atomic vapours is one of these systems that have been studied for decades and have only recently been shown to be the scene of L\'{e}vy flights.

Abstract:
Quantum protocols will be more efficient with high-dimensional entangled states. Photons carrying orbital angular momenta can be used to create a high-dimensional entangled state. In this paper we experimentally demonstrate the entanglement of the orbital angular momentum between the Stokes and anti-Stokes photons generated in a hot atomic ensemble using spontaneous four-wave-mixing. This experiment also suggests the existence of the entanglement concerned with spatial degrees of freedom between the hot atomic ensemble and the Stokes photon.

Abstract:
A scheme for the generation of non-classical pairs of photons in atomic vapours is proposed. The scheme exploits the fact that the cross correlation of the emission of photons from the extreme transitions of a four-level cascade system shows anti-bunching which has not been reported earlier and which is unlike the case of the three level cascade emission which shows bunching. The Cauchy-Schwarz inequality which is the ratio of cross-correlation to the auto correlation function in this case is estimated to be $10^3-10^6$ for controllable time delay, and is one to four orders of magnitude larger compared to previous experiments. The choice of Doppler free geometry in addition to the fact that at three photon resonance the excitation/deexcitation processes occur in a very narrow frequency band, ensures cleaner signals.

Abstract:
We present theoretical and experimental results of L\'evy flights of light originating from a random walk of photons in a hot atomic vapor. In contrast to systems with quenched disorder, this system does not present any correlations between the position and the step length of the random walk. In an analytical model based on microscopic first principles including Doppler broadening we find anomalous L\'evy-type superdiffusion corresponding to a single-step size distribution P(x) proportional to x^(-1-alpha), with alpha=1. We show that this step size distribution leads to a violation of Ohm's law [T_(diff) proportional to L^(-alpha/2) different from 1/L], as expected for a L\'evy walk of independent steps. Furthermore the spatial profile of the transmitted light develops power law tails [I(r) proportional to r^(-3-alpha)]. In an experiment using a slab geometry with hot rubidium vapor, we measured the total diffuse transmission T_(diff) and the spatial profile of the transmitted light T_{diff}(r). We obtained the microscopic L\'evy parameter alpha under macroscopic multiple scattering conditions paving the way to investigation of L\'evy flights in different atomic physics and astrophysics systems.

Abstract:
We report a thorough investigation into the absorptive and dispersive properties of hot caesium vapour, culminating in the development of a simple analytical model for off-resonant Faraday rotation. The model, applicable to all hot alkali metal vapours, is seen to predict the rotation observed in caesium, at temperatures as high as 115 $^{\circ}$C, to within 1% accuracy for probe light detuned by greater than 2 GHz from the $D_{2}$ lines. We also demonstrate the existence of a weak probe intensity limit, below which the effect of hyperfine pumping is negligible. Following the identification of this regime we validate a more comprehensive model for the absorption and dispersion in the vicinity of the $D_{2}$ lines, implemented in the form of a computer code. We demonstrate the ability of this model to predict Doppler-broadened spectra to within 0.5% rms deviation for temperatures up to 50 $^{\circ}$C.

Abstract:
A semi-classical theory of coherent light scattering from an elongated sample of cold atoms exposed to an off-resonant laser beam is presented. The model, which is a direct extension of that of the collective atomic recoil laser (CARL), describes the emission of two superradiant pulses along the sample's major axis simultaneous with the formation of a bidimensional atomic grating inside the sample. It provides a simple physical picture of the recent observation of collective light scattering from a Bose-Einstein condensate [S. Inouye et al., Science N.285, p. 571 (1999)]. In addition, the model provides an analytical description of the temporal evolution of the scattered light intensity which shows good quantitative agreement with the experimental results of Inouye et al.

Abstract:
We investigate multiple scattering of near-resonant light in a Doppler-broadened atomic vapor. We experimentally characterize the length distribution of the steps between successive scattering events. The obtained power law is characteristic of a superdiffusive behavior, where rare but very long steps (L\'evy flights) dominate the transport properties.

Abstract:
We present protocols for creating entangled states of two modes of the electromagnetic field, by using a beam of atoms crossing microwave resonators. The atoms are driven by a transverse, classical field and pump correlated photons into (i) two modes of a cavity and (ii) the modes of two distant cavities. The protocols are based on a stochastic dynamics, characterized by random arrival times of the atoms and by random interaction times between atoms and cavity modes. The resulting effective model yields a master equation, whose steady state is an entangled state of the cavity modes. In this respect, the atoms act like a quantum reservoir, pulling the cavity modes into an entangled, Einstein-Podolski-Rosen (EPR) state, whose degree of entanglement is controlled by the intensity and the frequency of the transverse field. This scheme is robust against stochastic fluctuations in the atomic beam, and it does not require atomic detection nor velocity selection.

Abstract:
We study the performance and limitations of a coherent interface between collective atomic states and single photons. A quantized spin-wave excitation of an atomic sample inside an optical resonator is prepared probabilistically, stored, and adiabatically converted on demand into a sub-Poissonian photonic excitation of the resonator mode. The measured peak single-quantum conversion efficiency of 0.84(11) and its dependence on various parameters are well described by a simple model of the mode geometry and multilevel atomic structure, pointing the way towards implementing high-performance stationary single-photon sources.

Abstract:
Cold atomic ensembles can mediate the generation of entanglement between pairs of photons. Photons with specific directions of propagation are detected, and the entanglement can reside in any of the degrees of freedom that describe the whole quantum state of the photons: polarization, spatial shape or frequency. We show that the direction of propagation of the generated photons determines the spatial quantum state of the photons and therefore, the amount of entanglement generated. When photons generated in different directions are combined, this spatial distinguishing information can degrade the quantum purity of the polarization or frequency entanglement.