Thermalization and breakdown of thermalization in photon condensates

Abstract

We examine in detail the mechanisms behind thermalization and Bose-Einstein condensation of a gas of photons in a dye-filled microcavity. We derive a microscopic quantum model, based on that of a standard laser, and show how this model can reproduce the behavior of recent experiments. Using the rate equation approximation of this model, we show how a thermal distribution of photons arises. We go on to describe how the non-equilibrium effects in our model can cause thermalization to break down as one moves away from the experimental parameter values. In particular, we examine the effects of changing cavity length, and of altering the vibrational spectrum of the dye molecules. We are able to identify two measures which quantify whether the system is in thermal equilibrium. Using these we plot "phase diagrams" distinguishing BEC and standard lasing regimes. Going beyond the rate equation approximation, our quantum model allows us to investigate both the second order coherence, g (2) , and the linewidth of the emission from the cavity. We show how the linewidth collapses as the system transitions to a Bose condensed state, and compare the results to the Schawlow-Townes linewidth.

Spontaneous Symmetry Breaking and Phase Coherence of a Photon Bose-Einstein Condensate Coupled to a Reservoir

“…In general, the photon statistics interpolates between Poissonian statistics for small reservoir sizes and a Bose-Einstein distribution for an infinitely large reservoir [24,26]. While for Poissonian statistics damped intensity fluctuations and macroscopic phase coherence of the condensate are expected [28][29][30][31], for the latter distribution the fluctuations become as large as the average photon numbern, i.e. ∆n =n.…”

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

“…Kirton and Keeling elaborated further results of their model [42], looking at the dynamics of photon populations after a pulsed pumping event, and evaluating both first-and second-order correlations for individual photon modes. In response to observations of the breakdown of thermalization due to inhomogeneous pumping, in both stationary [34] and time-resolved experiments [35], they modified their model to include spatial distributions of pumping and molecular excitation [43].…”

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

“…4 and 6), the system can act as an optomechanical-assisted laser without inversion [49]. In these cases, since the phase transition is in nonequilibrium, the macroscopic population is not necessarily in the ground state of the cavity [30].…”

“…Some of these studies have concentrated on the modeling of the photon BEC from the point of view of equilibrium statistical mechanics [15,[21][22][23][24][25], and some other theoretical works have explored such topics as the emergence of phase coherence in photon BEC resulting from photon-photon interaction through an intermediate medium [26], phase diffusion in a BEC of light in a dye-filled optical microcavity [27], quantum modeling of the nonequilibrium BEC of photons and polaritons in planar microcavity devices [28], and the crossover from photon condensation to laser-like states [29,30]. BEC and laser operation have similar features because both of them involve a spontaneous phase-symmetry breaking and a transition to a macroscopically occupied quantum state.…”