Subradiance in a Large Cloud of Cold Atoms

Abstract

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.

Exact electrodynamics versus standard optics for a slab of cold dense gas

“…Our hypothesis is that there are two in principle independent dimensionless density parameters in the light-propagation problem, the on-resonance optical thickness 6πρh (6πρhk −2 in terms of full dimensional quantities) that is a MFT parameter, and the plain ρ (ρk −3 ) that governs the role of dipole-dipole interactions beyond MFT. In several recent experiments [3][4][5]10] the on-resonance optical thickness has proven to be the dimensionless parameter that governs the density dependence of the results. In contrast, our interpretation is that the nontrivial results in Fig.…”

“…Optical thickness is a characteristic dimensionless parameter of MFT, and while MFT remains valid, optical thickness may be expected to be the dimensionless parameter. Numerous theoretical analyses are phrased in terms of optical thickness, and a scaling with optical thickness has been demonstrated in recent experiments, e.g., [3][4][5]10]. It is not a surprise that one can observe superradiance even in standard optics, and that it scales with optical thickness; optical thickness makes optical resonances broader, whereupon the conventional wisdom about Fourier transformations automatically predicts shortening time scales.…”

“…Therefore the delta function divergence in G, if any, should have no effect on P(r 1 ) solved from Eq. (5). By an analogous argument, the delta function divergence has no effect on P 2 (r 1 ; r 2 ), and so forth.…”

“…This subject is obviously very old, but cold atomic samples afford an opportunity for experiments in unprecedented regimes and in unprecedented detail. Correspondingly, new experiments are emerging rapidly [1][2][3][4][5][6][7][8][9][10]. The measurements of the optical response have been dominated by trapped inhomogeneous atomic ensembles, but also those with atoms confined in a slab geometry are emerging in increasing numbers in both thermal vapor cells using a hot gas [11] and in the ultracold regime [12].…”

Collective effects in the radiation pressure force

“…Starting from an independent approach, cooperative scattering in the low-intensity (or 'single-photon') regime, related to Dicke states [16], has been investigated in the mid 2000s, first from a theoretical point of view [17], followed by experiments with presently ongoing efforts in many groups [18][19][20][21][22][23][24][25][26][27][28][29]. One result, which has been described with a cooperative scattering approach, has been the momentum transfer onto the center of mass of a cloud of cold atoms, measured via the radiation pres-scattering has been developed [33,34].…”