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arXiv:cond-mat/0601289 · Physical Review A

Force on a moving point impurity due to quantum fluctuations in a Bose-Einstein condensate

David C K Roberts

Published Jul 17, 2006• 13 citations
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Abstract

An analytic expression is derived for a force on a weak point impurity arising from the scattering of quantum fluctuations in a slow-moving, weakly interacting, three-dimensional Bose-Einstein condensate at zero temperature. In an infinitely extended geometry, this force is shown to exist at any arbitrarily small flow velocity below Landau's critical velocity. Furthermore, this force is shown to be directly proportional to the flow speed.

DOI
10.1103/physreva.74.013613

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An analytic expression is derived for a force on a weak point impurity arising from the scattering of quantum fluctuations in a slow-moving, weakly interacting, three-dimensional Bose-Einstein condensate at zero temperature. In an infinitely extended geometry, this force is shown to exist at any arbitrarily small flow velocity below Landau's critical velocity. Furthermore, this force is shown to be directly proportional to the flow speed.
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 study the drag force acting on an impurity moving through a 1D Bose-Einstein condensate in the presence of both quantum and thermal fluctuations. We are able to find exact analytical solutions of the partial differential equations to the level of the Bogoliubov approximation. At zero temperature, we find a nonzero force is exerted on the impurity at subcritical velocities, due to the scattering of quantum fluctuations. We make the following explicit assumptions: far from the impurity the system is in a quantum state given by that of a zero (or finite) temperature Bose-Einstein condensate, and the scattering process generates only causally related reflection/transmission. The results raise unanswered questions in the quantum dynamics associated with the formation of persistent currents.
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.
The existence of frictionless flow below a critical velocity for obstacles moving in a superfluid is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a nonzero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consistent extension of Bogoliubov theory to second order in the interaction strength, and finds new analytical solutions to the Bogoliubov-de Gennes equations for a gray soliton. Our results raise questions regarding the quantum dynamics in the formation of persistent currents in superfluids.
Abstract We study the hydrodynamic forces acting on a small impurity moving in a two-dimensional Bose–Einstein condensate at non-zero temperature. The condensate is modelled by the damped-Gross Pitaevskii (dGPE) equation and the impurity by a Gaussian repulsive potential coupled to the condensate. For weak coupling, we obtain analytical expressions for the forces acting on the impurity, and compare them with those computed through direct numerical simulations of the dGPE and with the corresponding expressions for classical forces. For non-steady flows, there is a time-dependent force dominated by inertial effects and which has a correspondence in the Maxey–Riley theory for particles in classical fluids. In the steady-state regime, the force is dominated by a self-induced drag. Unlike at zero temperature, where the drag force vanishes below a critical velocity, at low temperatures the impurity experiences a net drag even at small velocities, as a consequence of the energy dissipation through interactions of the condensate with the thermal cloud. This dissipative force due to thermal drag is similar to the classical Stokes’ drag. There is still a critical velocity above which steady-state drag is dominated by acoustic excitations and behaves non-monotonically with impurity’s speed.