Bose condensation in nonequilibrium quantum gases: An adventure in the thermodynamics of light and matter

Abstract

Nonequilibrium condensates in microcavities have been extensively analysed over the past decades. Like equilibrium condensates, they are characterised by a macroscopic population of the ground state, however, the system is subjected to gain and loss through the finite lifetime of the microcavity. In these systems, a Bose gas is an open system in which heat and particles are continually exchanged with reservoirs. Based on the collection of knowledge of their kinetics provided by simulations and by experimental works, we show that these gases act as thermal machines whose output power is coherent emission of light. As in the case of a laser, these thermal machines are constrained by the second law of thermodynamics and operate with efficiency bounded by the Carnot limit.

We considered in depth condensation of both exciton-polaritons and photons. Starting with polaritons, we constructed a few-level model that captures the main processes involved in the buildup of a ground state population. The model consists of a three-level system interacting with a field and connected to a hot and a cold thermal reservoir, that represents a non-resonant pump and the lattice phonons. This subsystem can drive a condensate, through polariton-polariton scattering, which produces work in the form of coherent light emission from the microcavity. We obtain a phase diagram as a function of the temperatures of the two baths and analyse the phase transition.

To extend the analysis to a photon gas we use a kinetic approach to show that condensation is also restricted by the second law of thermodynamics and that, with a resonant pump, it can be mapped to a three-level heat engine model. We continue the analysis by exploring the effects of altering the pump on the steady state of the system. We show that condensation can be achieved using sunlight as a source and obtain its efficiency.

Our results elucidate a new link between nonequilibrium condensation and lasers. Beyond that, we also discuss the connection of these phenomena with synchronisation.