Finite-size effects in one-dimensional Bose-Einstein condensation of photons

TL;DR

This paper provides an analytical approach to accurately describe finite-size effects in one-dimensional photon Bose-Einstein condensation, improving theoretical predictions of critical parameters and reconciling theory with experimental results.

Contribution

It introduces an analytical continuation method to account for higher-order finite-size corrections in 1D photon BEC, addressing divergence issues in previous analyses.

Findings

Higher-order corrections reduce the discrepancy between theory and experiment.

Analytical expressions for critical temperature and particle number are derived.

Finite-size effects are crucial for understanding BEC in one-dimensional systems.

Abstract

The Bose-Einstein condensation (BEC) of photons has been realized in one- and two-dimensional systems. When considering the influence of finite-size effect, the condensation in the one-dimensional fibre is of special interest since such a condensation cannot occur in the thermodynamic limit due to the linear dispersion relation of photons. The finite-size effect must play a key role in this system and needs a detailed description. However, the previous theoretical analysis of finite-size effect is often not accurate enough and only gives the leading-order contribution due to a divergence difficulty. In this paper, by using an analytical continuation method to overcome the divergence difficulty, we give an analytical treatment for the finite-size effect in BEC. The analytical expressions of the critical temperature or critical particle number with higher order correction and the chemical potential below the transition point are presented. Our result shows that in a recent experiment, the deviation between experiment and theory is overestimated, most of which is caused by the inaccurate theoretical treatment of the finite-size effect. By taking into account the next-to-leading correction, we find that the actual deviation is much smaller.