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arXiv:1408.5826 · Journal of Physics B Atomic Molecular and Optical Physics

Casimir effect for a Bose–Einstein condensate inside a cylindrical tube

Shyamal Biswas, Saugata Bhattacharyya, Amit Agarwal

Published Nov 24, 2015• 1 citation
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Abstract

Abstract We explore the Casimir effect on an interacting Bose–Einstein condensate (BEC) inside a cylindrical tube. The Casimir force for the confined BEC consists of (i) a mean-field part arising from the spatial inhomogeneity of the condensate order parameter, and (ii) a quantum fluctuation part arising from the confinement of Bogoliubov excitations in the condensate. Our analytical result predicts Casimir force on a cylindrical shallow of 4 He well below the λ -point, and can be tested experimentally.

DOI
10.1088/0953-4075/49/1/015301

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Abstract We explore the Casimir effect on an interacting Bose–Einstein condensate (BEC) inside a cylindrical tube. The Casimir force for the confined BEC consists of (i) a mean-field part arising from the spatial inhomogeneity of the condensate order parameter, and (ii) a quantum fluctuation part arising from the confinement of Bogoliubov excitations in the condensate. Our analytical result predicts Casimir force on a cylindrical shallow of 4 He well below the λ -point, and can be tested experimentally.
The Casimir force due to thermal fluctuations (or the pseudo-Casimir force) was previously calculated for a perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to quantum fluctuations in a weakly-interacting dilute Bose–Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections to the leading-order result which we refer to as Bogoliubov corrections. The leading-order term is identified as the Casimir energy of a massless scalar field moving with a wave velocity equal to the speed of sound in the BEC. We then obtain the leading-order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary length and obtain the finite-size correction to the parallel plate scenario.
Considering the Casimir effect due to phononic excitations of a weakly interacting dilute Bose–Einstein condensate (BEC), we derive a renormalized expression for the zero-temperature Casimir energy 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, smoothly describes the transition from the weakly interacting Bogoliubov regime to the non-interacting ideal BEC. For the weakly interacting case, 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.
We discuss a Casimir force due to zero-temperature quantum fluctuations in an interacting quasi–one-dimensional Bose-Einstein condensate (BEC). For the first time, we can investigate the effect of the trapping potential and the atom-atom interaction simultaneously both of which contribute to the Casimir force. Furthermore, we calculate the Casimir force due to thermal fluctuations at finite temperature. Finally, we speculate on some possible experimental realization and detection of the force in future experiments.
We consider the Casimir force between two vortices due to the presence of density fluctuations induced by turbulent modes in a Bose–Einstein condensate. We discuss the cases of unbounded and finite condensates. Turbulence is described as a superposition of elementary excitations (phonons or BdG modes) in the medium. Expressions for the Casimir force between two identical vortex lines are derived, assuming that the vortices behave as point particles. Our analytical model of the Casimir force is confirmed by numerical simulations of the Gross–Pitaevskii equation, where the finite size of the vortices is retained. Our results are valid in the mean-field description of the turbulent medium. However, the Casimir force due to quantum fluctuations can also be estimated, assuming the particular case where the occupation number of the phonon modes in the condensed medium is reduced to zero and only zero-point fluctuations remain.