Critical velocity of superfluid flow through single barrier and periodic potentials

TL;DR

This paper derives an analytic expression for the critical velocity of superfluid flow through barriers and periodic potentials in ultracold gases, validated by numerical solutions and relevant for experimental setups.

Contribution

It introduces a hydrodynamic LDA-based model for predicting critical velocities in superfluids with barriers, applicable to Bose and Fermi gases, and compares it with numerical solutions.

Findings

Analytic expression for critical current as a function of potential parameters.

Identification of flow regimes: hydrodynamic, quantum, and tunneling.

Validation of the model with numerical solutions of Gross-Pitaevskii and Bogoliubov-de Gennes equations.

Abstract

We investigate the problem of an ultracold atomic gas in the superfluid phase flowing in the presence of a potential barrier or a periodic potential. We use a hydrodynamic scheme in the local density approximation (LDA) to obtain an analytic expression for the critical current as a function of the barrier height or the lattice intensity, which applies to both Bose and Fermi superfluids. In this scheme, the stationary flow becomes energetically unstable when the local superfluid velocity is equal to the local sound velocity at the point where the external potential is maximum. We compare this prediction with the results of the numerical solutions of the Gross-Pitaevskii and Bogoliubov-de Gennes equations. We discuss the role of long wavelength excitations in determining the critical velocity. Our results allow one to identify the different regimes of superfluid flow, namely, the LDA hydrodynamic regime, the regime of quantum effects beyond LDA for weak barriers and the regime of tunneling between weakly coupled superfluids for strong barriers. We finally discuss the relevance of these results in the context of current experiments with ultracold gases.