Robustness of Dicke subradiance against thermal decoherence

Abstract

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...

Dephasing-assisted entanglement in a system of strongly coupled qubits

“…Note that the simple model developed in this work may shed light on the recently demonstrated robustness of the subradiant state decay time for an ensemble of cold atoms with the increasing of temperature [51]. In this regard, the toy-model that describes long-lived entanglement may be useful for qualitative analyses.…”

Optical response of atom chains beyond the limit of low light intensity: The validity of the linear classical oscillator model

“…We find that the slope (n lin C − n C )/(n C I in ) has a pronounced dependence on which collective mode is driven, with a smaller υ α resulting in a larger slope in all but one case. 2 The drive mode-matched to the υ α = 0.96γ mode, for example, results in appreciable deviation between n C and n lin C at intensities I in 0.02I s , whereas a drive modematched to the most superradiant mode (υ α = 1.41γ) shows similar deviation at thrice this intensity. A more extreme case occurs when the lattice spacing is increased to a = 0.6λ.…”

“…can scatter coherently multiple times between the resonators, resulting in strong light-mediated, long-range interactions. This provides a highly controllable system to explore classical and quantum many-body physics, which has been shown to boast subradiance [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and other collective phenomena in trapped atomic ensembles and in resonator arrays [38][39][40][41], with potential applications to quantum information processing [42][43][44], the studies of nontrival topological phases [45][46][47], and atomic clocks [48][49][50][51].…”

Quantum collective effects in a dilute cloud of two-level atoms interacting with a classical light

“…[57][58] The cooperative scattering of light 18 leads to many-body effects with a rich physics. Since Dicke's work on coherence in the spontaneous emission superradiance 9,15,[59][60] , an enhancement in the field emission with collective decay rate larger than the single atom one Γ N > Γ, and its counterpart subradiance 10,[61][62][63] Γ N < Γ have been studied both from the theoretical 12, 64-65 and experimental 10, 66-67 side. However, most of the work in the literature were performed in the linear optics limit, with at most one excitation in the system and, in particular for the radiated far-field intensity, its decay dynamics is well understood in the switch-off protocol, thus there is no Rabi oscillations after the laser is turned off.…”

“…24 we compare the experimental signal with MF and CD simulations for higher saturation parameter s. From the experimental side, the same setup described in section 4.1.1.1 is used with some upgrades. [61][62] The experiment is still in development for high saturation parameter and some issues, for example, higher temperature in the system and higher laser switch-on time (17ns), are being addressed to study this regime with a better control of the different parameters. Note that, increasing the saturation parameter ( Fig.…”