On the hydrodynamics of nonlinear gaugecoupled quantum fluids
Abstract
By constructing a hydrodynamic canonical formalism, we show that the occurrence of an arbitrary densitydependent gauge potential in the meanfield Hamiltonian of a Bosecondensed fluid invariably leads to nonlinear flowdependent 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 opticallyaddressed twolevel atoms. In the Cauchy equation of mechanical momentum transport of the superfluid, two nontrivial terms emerge due to the densitydependent vector potential. A bodyforce 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 innerproduct 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 nontrivial local phase, which is antisymmetric under reversal of the gauge potential. The phase profile leads to a canonicalflow or phaseflow 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.
Contribution to the Topical Issue "Topological Ultracold Atoms and Photonic Systems", edited by G. Juzeliūnas, R. Ma, Y.J. Lin and T. Calarco.
 Publication:

European Physical Journal D
 Pub Date:
 May 2020
 DOI:
 10.1140/epjd/e20201005243
 Bibcode:
 2020EPJD...74...92B