Casimir Force between Two Vortices in a Turbulent Bose–Einstein Condensate

José Tito Mendonça,João D Rodrigues,Hugo Terças,Arnaldo Gammal

doi:10.3390/atoms8040077

Abstract

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.

Highlights

The concept of quantum vacuum plays a central role in modern physics and the Casimir force is a direct manifestation of its properties
Bose–Einstein condensates (BEC) with a graphene sheet [13], and the motion of impurity atoms in a BEC [14] were studied. We introduce another configuration relevant to BECs, by considering the contribution of the Casimir force to the interaction between two vortices in a turbulent BEC. This is directly relevant to the important problem of vortex-vortex interactions [15,16,17], which has been a central issue on quantum turbulence in superfluids and condensates [18]
Since the condensate density vanishes at the centre of the vortex core, one expects a complex structure of modes that are consistent with the condition of vanishing density at the vortex core. This will lead to a vortex repulsion, rooted in a mechanism that is analogous to the well known Casimir effect between conducting plates in vacuum, as we shall demonstrate via numerical simulations of the Gross–Pitaevskii equation

Summary

Introduction

The concept of quantum vacuum plays a central role in modern physics and the Casimir force is a direct manifestation of its properties. BEC with a graphene sheet [13], and the motion of impurity atoms in a BEC [14] were studied We introduce another configuration relevant to BECs, by considering the contribution of the Casimir force to the interaction between two vortices in a turbulent BEC. This is directly relevant to the important problem of vortex-vortex interactions [15,16,17], which has been a central issue on quantum turbulence in superfluids and condensates [18]. On a more phenomenological basis, we will be able to discuss the case of quantum fluctuations, considered as a particular case of the turbulent fluctuations where the occupation number of the quantised BdG modes tends to zero, and only the zero-point fluctuations of the quantised field remain

Theoretical Model

Numerical Simulations

Conclusions