Critical velocity for superfluidity in the one-dimensional mean-field regime: From matter to light quantum fluids

TL;DR

This paper nonperturbatively determines the critical velocity for superfluidity in one-dimensional quantum fluids flowing past obstacles, providing exact solutions and numerical methods applicable to matter and light-based quantum fluids.

Contribution

It introduces a nonperturbative approach to calculate the critical velocity in 1D quantum fluids, including exact expressions and a numerical interpolation method.

Findings

Exact expressions for critical velocity in narrow and wide obstacle limits

Numerical interpolation method for intermediate regimes

Agreement with full numerics when including particle losses

Abstract

We determine in a nonperturbative way the critical velocity for superfluidity of a generic quantum fluid flowing past a localized obstacle in the one-dimensional mean-field regime. We get exact expressions in the narrow- and wide-obstacle limits and interpolate them numerically using an original relaxation algorithm for the stationary problem. The existence of a Josephson-type critical current across a very high and slowly varying obstacle is discussed. Particle losses, if present, are treated within an adiabatic approach of the dynamics giving results in excellent agreement with full numerics. Relevant for experiments with quantum fluids of matter, of mixed matter-light, and of light, our study paves the way for further nonperturbative investigations in higher dimensions and beyond mean-field theory.