Bose-Einstein condensation of photons in an ideal atomic gas

TL;DR

This paper investigates the thermodynamic equilibrium conditions for Bose-Einstein condensation of photons in an ideal atomic gas, revealing two distinct regimes of transition temperature dependence and providing analytical and numerical insights into the phenomenon.

Contribution

It derives general equilibrium equations, identifies two regimes of photon Bose condensation, and analyzes their conditions and characteristics in ideal atomic gases.

Findings

Two regimes of photon Bose condensation with different temperature dependence.

Analytical solutions for critical temperature in specific cases.

Photon condensation likely follows a logarithmic regime in many physical systems.

Abstract

We study peculiarities of Bose-Einstein condensation of photons that are in thermodynamic equilibrium with atoms of noninteracting gases. General equations of the thermodynamic equilibrium of the system under study are obtained. We examine solutions of these equations in the case of high temperatures, when the atomic components of the system can be considered as nondegenerated ideal gases of atoms, and the photonic component can form a state with the Bose condensate. Transcendental equation for transition temperature and expression for the density of condensed photons in the considered system are derived. We also obtain analytical solutions of the equation for the critical temperature in a number of particular cases. The existence of two regimes of Bose condensation of photons, which differ significantly in nature of transition temperature dependence on the total density of photons pumped into the system, is revealed. In one case, this dependence is a traditional fractional-power law, and in another one it is the logarithmic law. Applying numerical methods, we determine boundaries of existence and implementation conditions for different regimes of condensation depending on the physical parameters of the system under study. We also show that for a large range of physical systems that are in equilibrium with photons (from ultracold gases of alkali metals to certain types of ideal plasma), the condensation of photons should occur according to the logarithmic regime.