Analytical theory of enhanced Bose-Einstein condensation in thin films

TL;DR

This paper develops an analytical theory for Bose-Einstein condensation in thin films, predicting high critical temperatures and new thermodynamic behaviors in nanoscale regimes, with potential for experimental realization.

Contribution

It provides closed-form expressions for the critical temperature and thermodynamic properties of BEC in thin films, including the prediction of high-temperature BEC and novel heat capacity behavior.

Findings

Critical temperature scales as L^{-1/2} in strong confinement.

Heat capacity of nano-scale films follows a T^2 law.

Condensate fraction follows a [1 - (T/T_c)^2] law.

Abstract

We present an analytically solvable theory of Bose-Einstein condensation in thin film geometries. Analytical closed-form expressions for the critical temperature are obtained in both the low-to-moderate confinement regime (where the film thickness $L$ is in the order of microns) as well as in the strong confinement regime where the thickness is in the order of few nanometers or lower. The possibility of high-temperature BEC is predicted in the strong confinement limit, with a square-root divergence of the critical temperature $T_{c} \sim L^{-1/2}$. For cold Bose gases, this implies an enhancement up to two orders of magnitude in $T_{c}$ for films on the nanometer scale. Analytical predictions are also obtained for the heat capacity and the condensate fraction. A new law for the heat capacity of the condensate, i.e. $C \sim T^{2}$, is predicted for nano-scale films, which implies a different $\lambda$ point behaviour with respect to bulk systems, while the condensate fraction is predicted to follow a $[1- (T/T_{c})^{2}]$ law.