Thermalization and Bose-Einstein condensation of quantum light in bulk nonlinear media

TL;DR

This paper investigates how quantum light in a nonlinear medium can thermalize and form a Bose-Einstein condensate, proposing an experimental setup for achieving this phenomenon as a new coherent light source.

Contribution

It introduces a theoretical framework linking quantum light propagation to Bose-Einstein condensation and proposes an experimental method for optical evaporative cooling.

Findings

Derived expressions for thermalization time, temperature, and chemical potential.

Established a connection between quantum light dynamics and Bose-Einstein statistics.

Proposed an optical setup for achieving Bose-Einstein condensation of light.

Abstract

We study the thermalization and the Bose-Einstein condensation of a paraxial, spectrally narrow beam of quantum light propagating in a lossless bulk Kerr medium. The spatiotemporal evolution of the quantum optical field is ruled by a Heisenberg equation analogous to the quantum nonlinear Schr\"odinger equation of dilute atomic Bose gases. Correspondingly, in the weak-nonlinearity regime, the phase-space density evolves according to the Boltzmann equation. Expressions for the thermalization time and for the temperature and the chemical potential of the eventual Bose-Einstein distribution are found. After discussing experimental issues, we introduce an optical setup allowing the evaporative cooling of a guided beam of light towards Bose-Einstein condensation. This might serve as a novel source of coherent light.