Superradiant optomechanical phases of cold atomic gases in optical resonators

TL;DR

This paper theoretically investigates superradiant light emission from cold atomic gases in optical resonators, considering mechanical effects, and identifies thresholds for different emission regimes including incoherent, coherent, and chaotic phases.

Contribution

It introduces a mean-field model incorporating mechanical effects to analyze superradiance thresholds and phase transitions in cold atomic gases within optical cavities.

Findings

Thermal fluctuations suppress superradiance above a threshold temperature.

Emission can be coherent or chaotic depending on pump rate below the threshold temperature.

Mechanical energy exchange leads to a superradiant decay rate threshold, affecting emission and matter-wave grating formation.

Abstract

We theoretically analyze superradiant emission of light from a cold atomic gas, when mechanical effects of photon-atom interactions are considered. The atoms are confined within a standing-wave resonator and an atomic metastable dipolar transition couples to a cavity mode. The atomic dipole is incoherently pumped in the parameter regime that would correspond to stationary superradiance in absence of inhomogeneous broadening. Starting from the master equation for cavity field and atomic degrees of freedom we derive a mean-field model that allows us to determine a threshold temperature, above which thermal fluctuations suppress superradiant emission. We then analyze the dynamics of superradiant emission when the motion is described by a mean-field model. In the semiclassical regime and below the threshold temperature we observe that the emitted light can be either coherent or chaotic, depending on the incoherent pump rate. We then analyze superradiant emission from an ideal Bose gas at zero temperature when the superradiant decay rate $\Lambda$ is of the order of the recoil frequency $\omega_R$. We show that the quantized exchange of mechanical energy between the atoms and the field gives rise to a threshold, $\Lambda_c$, below which superradiant emission is damped down to zero. When $\Lambda>\Lambda_c$ superradiant emission is accompanied by the formation of matter-wave gratings diffracting the emitted photons. The stability of these gratings depends on the incoherent pump rate $w$ with respect to a second threshold value $w_c$. For $w>w_c$ the gratings are stable and the system achieves stationary superradiance. Below this second threshold the coupled dynamics becomes chaotic. We characterize the dynamics across these two thresholds and show that the three phases we predict (incoherent, coherent, chaotic) can be revealed via the coherence properties of the light at the cavity output.