Nonequilibrium Model of Photon Condensation

Abstract

We develop a nonequilibrium model of condensation and lasing of photons in a dye filled microcavity. We examine in detail the nature of the thermalization process induced by absorption and emission of photons by the dye molecules, and investigate when the photons are able to reach a thermal equilibrium Bose-Einstein distribution. At low temperatures, or large cavity losses, the absorption and emission rates are too small to allow the photons to reach thermal equilibrium and the behavior becomes more like that of a conventional laser. DOI: 10.1103/PhysRevLett.111.100404 PACS numbers: 03.75.Hh, 42.55.Mv, 67.85.Hj, 71.38.Àk Bose-Einstein condensation (BEC) has been observed in a wide variety of systems, from ultracold atomic gases [1,2] to quasiparticles in solid state systems such as polaritons [3][4][5][6], excitons [7], and magnons [8]. Recently experiments have shown convincing evidence of a BoseEinstein distribution, and macroscopic occupation of the lowest mode for a gas of photons confined in a dye-filled optical microcavity [9][10][11][12]. In these experiments, the thermal equilibrium distribution of photons arises because of phonon dressing of the absorption and emission by the dye molecules, and the rapid thermalization of rovibrational modes of the dye molecules by their collisions with the solvent. This leads to the accumulation of low-energy photons, closely following a Bose-Einstein distribution, as is clearly seen experimentally [10].Such a system is very closely related to a dye laser [13], but differs in the near-thermal emission spectrum that is observed below and near the threshold density and in the fact that the macroscopic population occurs at the minimum energy mode of the cavity and is not related to the gain maximum of the dye [10]. There are also close connections to microlasers [14]. However microlasers, having strong coupling between the gain medium and cavity, display thresholdless lasing [15]. In contrast, the observed behavior in the photon condensate [10] is that there is a sharp threshold which occurs far below inversion.In the context of polariton condensation [3][4][5][6] there has been much debate [16,17] about the extent to which the lack of true thermal equilibrium in experiments means the system should be called a condensate or a laser. However, various calculations for polaritons, from quantum kinetics [18,19] to Schwinger-Keldysh path integrals [20], have found a relatively smooth crossover between behavior typical of a laser, and that typical of an equilibrium condensate. Both lasers and condensates involve a spontaneous phase-symmetry breaking, and a transition to a macroscopically occupied mode, and so their connection has long been recognized [21]. The photon condensate system provides a further example of a system in which the distinction between Bose condensation and lasing must be carefully examined.The nature of the thermalization process in the photon condensate differs significantly from that found in other systems which exhibit BEC. There are no direct photon...

Quantum Langevin model for nonequilibrium condensation

“…Extensions of this theory including more complicate emitters can be used to describe the dye molecules involved in the photon condensation experiments of [5]. Several possibilities in this direction are explored in [21,45].…”

“…From the theoretical point of view, the recent work [21] has quantitatively explored the crossover from the equilibriumlike regime of [5] where the particle distribution closely follow the Bose-Einstein distribution, to non-equilibrium regimes where the distribution is more and more distorted up to the standard laser regime: in particular, the ratio between the thermalisation rate (encoded by the absorption/emission rates) and the pumping and photon losses was identified as the key parameter determining the equilibrium vs. nonequilibrium nature of the momentum distribution of photons.…”

Collective phases of strongly interacting cavity photons

“…For example, thermal equilibrium is essentially never a reasonable assumption in photonic systems, where dissipation must be countered by active pumping [10]. Indeed, the inadequacy of equilibrium descriptions for photonic systems has long been recognized [11], even though close analogies to thermal systems sometimes exist [12][13][14][15][16].Until recently, photonic systems have been restricted to a weakly interacting regime. With notable progress towards generating strong optical nonlinearities at the few-photon level, for example with atoms coupled to small-mode-volume optical devices [17][18][19][20][21][22], Rydberg polaritons [23,24], and circuit-QED devices [25][26][27][28], this situation is rapidly changing.…”

“…For example, thermal equilibrium is essentially never a reasonable assumption in photonic systems, where dissipation must be countered by active pumping [10]. Indeed, the inadequacy of equilibrium descriptions for photonic systems has long been recognized [11], even though close analogies to thermal systems sometimes exist [12][13][14][15][16].…”

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

“…Experimentally, grand canonical conditions in the condensed phase have been realized in a photon Bose-Einstein condensate coupled to a dye medium [19,20], where thermalization of the photon gas is achieved by absorption and re-emission processes on dye molecules [21][22][23].…”