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.

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.

We report the first realization of a guided quasicontinuous atom laser by rf outcoupling a BEC, from a hybrid optomagnetic trap into a horizontal atomic waveguide. This configuration allows us to cancel the acceleration due to gravity and keep the de Broglie wavelength constant at 0.5 µm during 0.1 s of propagation. We also show that our configuration, equivalent to pigtailing an optical fiber to a (photon) semiconductor laser, ensures an intrinsically good transverse mode matching.PACS numbers: 03.75. Pp, 39.20.+q, 42.60.Jf,41.85.Ew The Bose-Einstein condensation of atoms in the lowest level of a trap represents the matter-wave analog to the accumulation of photons in a single mode of a laser cavity. In analogy to photonic lasers, atom lasers can be obtained by outcoupling from a trapped Bose-Einstein condensate (BEC) to free space [1,2,3]. However, since atoms are massive particles, gravity plays an important role in the laser properties: in the case of rf outcouplers, it lies at the very heart of the extraction process [4] and in general, the beam is strongly accelerated downwards, causing a rapid decrease of the de Broglie wavelength. With the growing interest in coherent atom sources for atom interferometry [5,6,7] and new studies of quantum transport phenomena [8,9,10,11,12,13,14] where large and well defined de Broglie wavelength are desirable, a better control of the atomic motion during its propagation is needed. One solution is to couple the atom laser into a horizontal waveguide, so that the effect of gravity is canceled, leading to the realization of a coherent matter wave with constant wavelength.We report in this letter on the realization of such a guided quasicontinuous atom laser, where the coherent source, i.e. the trapped BEC, and the guide are merged together in a hybrid combination of a magnetic Ioffe-Pritchard trap and a horizontally elongated far offresonance optical trap constituting an atomic waveguide (see Fig. 1). The BEC, in a state sensitive to both trapping potentials, is submitted to a rf outcoupler yielding atoms in a state sensitive only to the optical potential, resulting in an atom laser propagating along the weak confining axis of the optical trap. In addition to canceling the effect of gravity, this configuration has several advantages. Firstly, coupling into a guide from a BEC rather than from a thermal sample [15] allows us to couple a significant flux into a small number of transverse modes of the guide. Secondly, the weak longitudinal trapping potential of the guide can be compensated by the antitrapping potential due to the second order Zeeman effect acting onto the outcoupled atoms, resulting in an atom laser with a quasiconstant de Broglie wavelength. Thirdly, using an rf outcoupler rather than releasing a BEC into a guide [14,16] results into quasicontinuous operation, thus insuring sharp linewidth, and gives a better control on the beam parameters. Indeed, changing the frequency of the outcoupler allows one to tune the value of the de Broglie wavelength of the atom...

International audienceCooperative scattering has been the subject of intense research in the last years. In this article, we discuss the concept of cooperative scattering from a broad perspective. We briefly review the various collective effects that occur when light interacts with an ensemble of atoms. We show that some effects that have been recently discussed in the context of 'single-photon superradiance', or cooperative scattering in the linear-optics regime, can also be explained by 'standard optics', i.e., using macroscopic quantities such as the susceptibility or the diffusion coefficient. We explain why some collective effects depend on the atomic density, and others on the optical depth. In particular, we show that, for a large and dilute atomic sample driven by a far-detuned laser, the decay of the fluorescence, which exhibits superradiant and subradiant dynamics, depends only on the on-resonance optical depth. We also discuss the link between concepts that are independently studied in the quantum-optics community and in the mesoscopic-physics community. We show that the coupled-dipole model predicts a departure from Ohm's law for the diffuse light, that incoherent multiple scattering can induce a saturation of fluorescence and we also show the similarity between the weak-localization correction to the diffusion coefficient and the inaccuracy of Lorentz local field correction to the susceptibility

We study the propagation of a noninteracting atom laser distorted by the strong lensing effect of the Bose-Einstein condensate (BEC) from which it is outcoupled. We observe a transverse structure containing caustics that vary with the density within the residing BEC. Using the WKB approximation, Fresnel-Kirchhoff integral formalism, and ABCD matrices, we are able to describe analytically the atom-laser propagation. This allows us to characterize the quality of the nonideal atom-laser beam by a generalized M2 factor defined in analogy to photon lasers. Finally we measure this quality factor for different lensing effects.

Properties of random and fluctuating systems are often studied through the use of Gaussian distributions. However, in a number of situations, rare events have drastic consequences, which can not be explained by Gaussian statistics. Considerable efforts have thus been devoted to the study of non Gaussian fluctuations such as Lévy statistics, generalizing the standard description of random walks. Unfortunately only macroscopic signatures, obtained by averaging over many random steps, are usually observed in physical systems. We present experimental results investigating the elementary process of anomalous diffusion of photons in hot atomic vapours. We measure the step size distribution of the random walk and show that it follows a power law characteristic of Lévy flights.

We report the first intensity correlation measured with star light since Hanbury Brown and Twiss' historical experiments. The photon bunching g (2) (τ, r = 0), obtained in the photon counting regime, was measured for 3 bright stars, α Boo, α CMi, and β Gem. The light was collected at the focal plane of a 1 m optical telescope, was transported by a multi-mode optical fiber, split into two avalanche photodiodes and digitally correlated in real-time. For total exposure times of a few hours, we obtained contrast values around 2 × 10 −3 , in agreement with the expectation for chaotic sources, given the optical and electronic bandwidths of our setup. Comparing our results with the measurement of Hanbury Brown et al. on α CMi, we argue for the timely opportunity to extend our experiments to measuring the spatial correlation function over existing and/or foreseen arrays of optical telescopes diluted over several kilometers. This would enable µas long-baseline interferometry in the optical, especially in the visible wavelengths with a limiting magnitude of 10.

We experimentally investigate the Bragg reflection of light at one-dimensionally ordered atomic structures by using cold atoms trapped in a laser standing wave. By a fine-tuning of the periodicity, we reach the regime of multiple reflection due to the refractive index contrast between layers, yielding an unprecedented high reflectance efficiency of 80%. This result is explained by the occurrence of a photonic band gap in such systems, in accordance with previous predictions.