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arXiv:cond-mat/0503706 · Physical Review Letters

Casimir-Like Force Arising from Quantum Fluctuations in a Slowly Moving Dilute Bose-Einstein Condensate

David C K Roberts, Yves Pomeau A

Published Sep 30, 2005• 75 citations
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Abstract

We calculate a force due to zero-temperature quantum fluctuations on a stationary object in a moving superfluid flow. We model the object by a localized potential varying only in the flow direction and model the flow by a three-dimensional weakly interacting Bose-Einstein condensate at zero temperature. We show that this force exists for any arbitrarily small flow velocity and discuss the implications for the stability of superfluid flow.

DOI
10.1103/physrevlett.95.145303

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We calculate a force due to zero-temperature quantum fluctuations on a stationary object in a moving superfluid flow. We model the object by a localized potential varying only in the flow direction and model the flow by a three-dimensional weakly interacting Bose-Einstein condensate at zero temperature. We show that this force exists for any arbitrarily small flow velocity and discuss the implications for the stability of superfluid flow.
We discuss a force arising from zero-temperature quantum fluctuations in a weakly interacting Bose-Einstein condensate (BEC). We argue that there is a drag force on an object moving at speeds well below Landau's critical velocity, and motivate our argument by an analogy to the Casimir force in an electromagnetic vacuum. We sketch the calculation of this force for an object described by a general potential. We comment about the relevance of our results to the stability of superfluid flow, arguing that this effect is consistent with the observation of persistent currents and that this effect introduces new experimental observables. Finally, we describe a new hydryodynamic boundary condition for superfluid flow that takes into account the scattering of quantum fluctuations off a rough surface.
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.
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.
It has been proposed in recent years that an impurity moving in a superfluid will experience drag forces even below the Landau critical velocity [1–3]. Quantum fluctuations that are present in superfluid systems at zero temperature can scatter from impurities present in the fluid. If the impurity is moving, there will be an asymmetric Doppler shift associated with the scattered waves, which will result in a net drag force. This challenges the long-accepted notion of dissipationless flow in superfluids. Analytical estimates of this drag force in superfluid Bose-Einstein condensates using Bogoliubov methods have found a non-zero drag force, resulting from the most sensible choice of boundary conditions in an infinite system. Through stochastic simulations of the 1D Bose gas under the truncated Wigner formalism, we verify the existence of this sub-critical drag force and quantify the drag forces present. We will also determine whether dissipationless flow can be recovered in finite sized systems.
We discuss a Casimir force due to zero-temperature quantum fluctuations in a weakly interacting Bose-Einstein condensate (BEC) with a strong harmonic trap. The results show that the presence of a strong harmonic trap changes the power law behavior of Casimir force due to the dimensional reduction effect. At finite temperature, we calculate Casimir force due to thermal fluctuation and find an exotic temperature dependent behavior in the first order term. Finally, we speculate some possible experimental realization and detection of the force in future experiments.