Casimir Energy of a BEC: From Moderate Interactions to the Ideal Gas

TL;DR

This paper derives an analytical expression for the Casimir energy in a Bose-Einstein condensate, capturing the transition from weak interactions to an ideal gas, and clarifies the role of phononic excitations in this phenomenon.

Contribution

It provides a re-normalized, analytical formula for the Casimir energy of a BEC that smoothly interpolates between interacting and non-interacting regimes.

Findings

Casimir energy reduces to phonon zero-point fluctuations in weakly interacting limit.

Casimir energy approaches zero for an ideal Bose gas.

Analytical density of modes computed for the confined BEC.

Abstract

Considering the Casimir effect due to phononic excitations of a weakly interacting dilute {BEC}, we derive a re-normalized expression for the zero temperature Casimir energy $\mathcal{E}_c$ of a {BEC} confined to a parallel plate geometry with periodic boundary conditions. Our expression is formally equivalent to the free energy of a bosonic field at finite temperature, with a nontrivial density of modes that we compute analytically. As a function of the interaction strength, $\mathcal{E}_c$ smoothly describes the transition from the weakly interacting Bogoliubov regime to the non-interacting ideal {BEC}. For the weakly interacting case, $\mathcal{E}_c$ reduces to leading order to the Casimir energy due to zero-point fluctuations of massless phonon modes. In the limit of an ideal Bose gas, our result correctly describes the Casimir energy going to zero.