Thermalization and Bose–Einstein condensation of a photon gas in a multimode hybrid atom-membrane optomechanical microcavity

Abstract

In this paper, we theoretically propose an optomechanical scheme to thermalize a two-dimensional photon gas in a hybrid optomechanical microcavity composed of a two-level atomic ensemble and a membrane oscillator enclosed in an optical cavity. The thermalization process is based on a phonon-induced asymmetry between the emission and the absorption rates of the atoms. We show that whenever this asymmetry obeys the detailed balance condition and if the photon lifetime is high enough, the steady-state photon number distribution matches the Bose-Einstein distribution. Furthermore, in order to study the effect of the optomechanical coupling on the Bose-Einstein condensation of photons, we calculate the critical photon number as a function of the temperature. We find that the optomechanically induced nonlinearity leads to the increase of the critical photon number, which can be controlled by tuning the optomechanical parameters.

Photon thermalization via laser cooling of atoms

“…Such work can be broadly classified into two categories that rely (i) on interactions between light and matter where the matter is in thermal equilibrium with an external reservoir, or (ii) multiple photon-photon collisions mediated by matter. The former includes the earliest theoretical proposal of photon BEC in a plasma [42], photon thermalization and condensation in a dye-filled microcavity [22,23,26,31,43], as well as recent proposals in quantum optomechanics [25,44]; the latter includes photon BEC through photon-photon scattering in a nonlinear resonator [45] and BEC of exciton polaritons [18][19][20] and stationary-light polaritons [21]. Our approach has the most in common with (i), however, it falls outside this category because the bath for the photons (i.e., the atoms) is not in thermal equilibrium with an external reservoir but rather driven to a nonequilibrium steady state with a thermal description.…”

Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers

“…There are a few outlandish theoretical proposals to combine photon BEC with quantum optomechanics [74,75] or atomic BEC [76,77] but, while not technically impossible, it is unlikely that anyone will go to the effort to implement the ideas experimentally.…”

Quantum dynamics of an optomechanical system in the presence of photonic Bose-Einstein condensate

“…In order to have a non-vanishing chemical potential and so a BEC of photons, it is necessary to have a thermalization mechanism in the micro-cavity, such as multiple absorption and reemission of photons by a dye solution [39,40] or other proposed thermalization schemes [55,56,60]. Here, we have assumed that the thermalization process takes place much faster than the optomechanical coupling, which is relevant for the typical experiment data [2,40].…”

“…Besides further relevant experimental investigations [42][43][44], various theoretical studies have been carried out to explain the equilibration and properties of the system in the framework of statistical mechanics [45][46][47], non equilibrium Green's function [48][49][50] and nonlinear Schrödinger equation [51,52]. In addition, some other theoretical schemes have been proposed to achieve thermalization and BEC phase transition of a photon gas in a dilute nondegenerated atomic gas [53], in a one-dimensional barrel optical microresonator filled with a dye solution [54], in an optomechanical cavity with a segmented moving mirror [55], and in a multimode hybrid atom-membrane optomechanical microcavity [56]. Furthermore, the temperature-dependent decay rate [57] and enhanced dynamic stark shift [58] of an atom interacting with a BEC of photons have been theoretically studied.…”