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

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.

12 pages, 3 figures, accepted for publication in JPA. New version with corrected typos and an additional appendix

References in corpus (2)

• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect
• External Fields as a Probe for Fundamental Physics

Cited by in corpus (4)

• Casimir effect in a dilute Bose gas in canonical ensemble within improved Hartree-Fock approximation
• Quantum Borderlines -- Fluctuation Energies in Ultracold Bose Gases
• Quantum vacuum effects in non-relativistic quantum field theory
• Density of condensate of a dilute Bose gas in improved Hartree-Fock approximation