Schwinger-Keldysh theory for Bose-Einstein condensation of photons in a dye-filled optical microcavity

TL;DR

This paper develops a theoretical framework using the Schwinger-Keldysh formalism to describe the dynamics and equilibrium properties of photon Bose-Einstein condensation in a dye-filled optical microcavity, accounting for finite photon lifetime effects.

Contribution

It introduces a Langevin field equation derived from the Schwinger-Keldysh formalism that captures photon dynamics, including damping effects due to finite photon lifetime, and applies it to analyze spectral functions and collective modes.

Findings

Finite lifetime effects are encapsulated in a damping parameter.

The theory predicts spectral functions in both normal and condensed phases.

Collective modes are characterized in the photon Bose-Einstein condensate.

Abstract

We consider Bose-Einstein condensation of photons in an optical cavity filled with dye molecules that are excited by laser light. By using the Schwinger-Keldysh formalism we derive a Langevin field equation that describes the dynamics of the photon gas, and in particular its equilibrium properties and relaxation towards equilibrium. Furthermore we show that the finite lifetime effects of the photons are captured in a single dimensionless damping parameter, that depends on the power of the external laser pumping the dye. Finally, as applications of our theory we determine spectral functions and collective modes of the photon gas in both the normal and the Bose-Einstein condensed phase.