Hydrodynamics of nonlinear gauge-coupled quantum fluids

TL;DR

This paper develops a hydrodynamic formalism for quantum fluids with density-dependent gauge potentials, revealing nonlinear flow effects, deriving momentum transport equations, and demonstrating how these influence superfluid groundstates and flow patterns.

Contribution

It introduces a canonical hydrodynamic framework for gauge-coupled quantum fluids, deriving new equations and analyzing effects of nonlinear gauge potentials on superfluid behavior.

Findings

Nonlinear flow-dependent terms appear in the wave equation due to density-dependent gauge potentials.

The derived momentum transport equation includes a dilation body-force and a flow pressure term.

Numerical simulations show gauge potentials induce asymmetric phase profiles and flow patterns around impurities.

Abstract

By constructing a hydrodynamic canonical formalism, we show that the occurrence of an arbitrary density-dependent gauge potential in the meanfield Hamiltonian of a Bose-condensed fluid invariably leads to nonlinear flow-dependent terms in the wave equation for the phase, where such terms arise due to the explicit dependence of the mechanical flow on the fluid density. In addition, we derive a canonical momentum transport equation for this class of nonlinear fluid and obtain an expression for the stress tensor. Further, we study the hydrodynamic equations in a particular nonlinear fluid, where the effective gauge potential results from the introduction of weak contact interactions in an ultracold dilute Bose gas of optically-addressed two-level atoms. In the Cauchy equation of mechanical momentum transport of the superfluid, two non-trivial terms emerge due to the density-dependent vector potential. A body-force of dilation appears as a product of the gauge potential and the dilation rate of the fluid, while the stress tensor features a canonical flow pressure term given by the inner-product of the gauge potential and the canonical current density. By numerical simulation, we illustrate an interesting effect of the nonlinear gauge potential on the groundstate wavefunction of a superfluid in the presence of a foreign impurity. We find that the groundstate adopts a non-trivial local phase, which is antisymmetric under reversal of the gauge potential. The phase profile leads to a canonical-flow or phase-flow dipole about the impurity, resulting in a skirting mechanical flow. As a result, the pressure becomes asymmetric about the object and the condensate undergoes a deformation.