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 experimentally and numerically study the temporal dynamics of light scattered by large clouds of cold atoms after the exciting laser is switched off, in the low intensity (linear-optics) regime. Radiation trapping due to multiple scattering as well as subradiance lead to decay much slower than the single atom fluorescence decay. These two effects have already been observed separately, but the interplay between them remained to be understood. Here, we show that with well chosen parameters of the driving field, the two effects can occur at the same time, but follow different scaling behaviors. The subradiant decay is observed at late time and its rate is independent of the detuning, while the radiation trapping decay is observed at intermediate time and depends on the detuning through the optical depth of the sample. Numerical simulations based on random walk process and coupled-dipole equations support our interpretations. Our study clarifies the different interpretations and physical mechanisms at the origin of slow temporal dynamics of light in cold atoms.

Cooperative scattering in cold atoms has gained renewed interest, in particular in the context of single-photon superradiance, with the recent experimental observation of super-and subradiance in dilute atomic clouds. Numerical simulations to support experimental signatures of cooperative scattering are often limited by the number of dipoles which can be treated, well below the number of atoms in the experiments. In this paper, we provide systematic numerical studies aimed at matching the regime of dilute atomic clouds. We use a scalar coupled-dipole model in the low excitation limit and an exclusion volume to avoid density-related effects. Scaling laws for super-and subradiance are obtained and the limits of numerical studies are pointed out. We also illustrate the cooperative nature of light scattering by considering an incident laser field, where half of the beam has a π phase shift. The enhanced subradiance obtained under such condition provides an additional signature of the role of coherence in the detected signal.

Subradiance is the cooperative inhibition of the radiation by several emitters coupled to the same electromagnetic modes. It has been predicted by Dicke in 1954 and only recently observed in cold atomic vapors. Here we address the question to what extend this cooperative effect survives outside the limit of frozen two-level systems by studying the subradiant decay in an ensemble of cold atoms as a function of the temperature. Experimentally, we observe only a slight decrease of the subradiant decay time when increasing the temperature up to several millikelvins, and in particular we measure subradiant decay rates that are much smaller than the Doppler broadening. This demonstrates that subradiance is surprisingly robust against thermal decoherence. The numerical simulations are in good agreement and allow us to extrapolate the behavior of subradiance at higher temperatures.Understanding the influence of decoherence or dephasing processes in cooperative effects such as super-and subradiance [1-7] is not only interesting from a fundamental point of view, but it is also important for the possible developments of photonic device exploiting cooperativity in the classical or quantum regime [8][9][10][11][12][13]. This is especially true if one wants to use solid-states devices [14,15], which are subject to phonon-induced decoherence. Previous theoretical studies of various toy models in the framework of open quantum systems have predicted some robustness of superradiance to noise and dephasing [16][17][18].In this Letter, we report an experimental study of thermal decoherence of subradiant Dicke states in large ensemble of cold atoms [4]. Indeed, even if laser-cooled atoms are not coupled to phonons, they are not completely frozen. Atomic motion has been shown to be a source of decoherence for coherent back-scattering [19] and to suppress the effect of recurrent scattering on the refractive index of dense atomic media [20,21]. Since subradiance is an interference effect involving very long time scales, it is expected to be particularly fragile.On the contrary, and quite surprisingly, we show here that subradiance in the linear-optics regime is robust against thermal motion. We observe only a slight decrease of the subradiant decay time when increasing the temperature up to several millikelvins, and in particular we measure subradiant decay rates Γ sub that are much smaller than the Doppler broadening Γ D , given by the width of the atomic velocity distribution. We also perform numerical simulations showing that the breakdown of subradiance only occurs when the Doppler broadening is on the same order of magnitude as the natural lifetime of the atomic transition Γ 0 . In practice, this means that subradiance can be observed and used at any "coldatom" temperature and even beyond.The experimental setup is based on a cloud of cold 87 Rb atoms prepared in a magneto-optical trap (MOT). After 60 ms of loading from the background vapor and a stage of compressed MOT (30 ms) we obtain a sample of N ≈ 3 × 10 9 atoms at a temperatu...

The theoretical description of the external degrees of freedom of atoms trapped inside a magnetooptical trap (MOT) often relies on the decoupling of the evolution of the internal and external degrees of freedom. That is possible thanks to much shorter timescales typically associated with the first ones. The electronic structure of alkaline-earth atoms, on the other hand, presents ultra-narrow transitions and metastable states that makes such an approximation invalid in the general case. In this article, we report on a model based on open Bloch equations for the evolution of the number of atoms in a magneto-optical trap. With this model we investigate the loading of the strontium blue magnetooptical trap under different repumping schemes, either directly from a Zeeman slower, or from an atomic reservoir made of atoms in a metastable state trapped in the magnetic quadrupolar field. The fluorescence observed on the strong 461 nm transition is recorded and quantitatively compared with the results from our simulations. The comparison between experimental results and calculations within our model allowed to identify the existence of the decay paths between the upper level of the repumping transition and the dark strontium metastable states, which could not be explained by electric dipole transition rates calculated in the literature. Moreover, our analysis pinpoints the role of the atomic movement in limiting the efficiency of the atomic repumping of the Sr metastable states.

No abstract

Abstract. We report a simple technique for stabilization of a laser frequency at the wings of an atomic resonance. The reference signal used for stabilization issues from interference effects obtained in a low-quality cavity filled with a resonant atomic vapour. For a frequency detuned at 2.6 GHz from the 133 Cs D 2 6S 1/2 F=4 to 6P 3/2 F'= 5 transition, the fractional frequency Allan deviation is 10 −8 for averaging times of 300 s, corresponding to a frequency deviation of 4 MHz. Adequate choice of the atomic density and of the cell thickness allows locking the laser at detunings larger than 10 GHz. Such a simple technique does not require magnetic fields or signal modulation.