Stationary through-flows in a Bose-Einstein condensate with a PT-symmetric impurity

TL;DR

This paper demonstrates the existence of stable stationary superfluid currents in a Bose-Einstein condensate with a PT-symmetric impurity, providing exact solutions and analyzing their stability and controllability.

Contribution

It introduces exact solutions for stationary through-flows in a PT-symmetric Bose-Einstein condensate and analyzes their stability and response to potential parameters.

Findings

Existence of two types of through-flow solutions: dip-like and hump-like.

Stable through-flow solutions form continuous families parametrized by flux.

Control of through-flows via gain-loss amplitude variations.

Abstract

Superfluid currents in the boson condensate with a source and sink of particles are modelled by the PT-symmetric Gross-Pitaevskii equation with a complex potential. We demonstrate the existence of through-flows of the condensate --- stationary states with the asymptotically nonvanishing flux. The through-flows come in two broad varieties determined by the form of their number density distribution. One variety is described by dip-like solutions featuring a localised density depression; the other one comprises hump-like structures with a density spike in their core. We exemplify each class by exact closed-form solutions. For a fixed set of parameters of the PT-symmetric potential, stationary through-flows form continuous families parametrized by the strength of the background flux. All hump-like and some dip-like members of the family are found to be stable. We show that the through-flows can be controlled by varying the gain-and-loss amplitude of the complex potential and that these amplitude variations may produce an anomalous response of the flux across the gain-loss interface.