Drag force on an impurity below the superfluid critical velocity in a quasi-one-dimensional Bose-Einstein condensate

TL;DR

This paper demonstrates that quantum and thermal fluctuations induce a non-zero drag force on an impurity in a quasi-one-dimensional Bose-Einstein condensate below the superfluid critical velocity, challenging the notion of frictionless flow.

Contribution

It extends Bogoliubov theory to second order, providing analytical solutions and revealing a persistent force due to fluctuation imbalances at all subcritical velocities and temperatures.

Findings

Quantum fluctuations cause a non-zero force on impurities below critical velocity.

The force is due to Doppler shift imbalances in reflected quantum fluctuations.

Analytical solutions to Bogoliubov-de Gennes equations for gray solitons are provided.

Abstract

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 non-zero 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.