Stationary states of a PT-symmetric two-mode Bose-Einstein condensate

TL;DR

This paper analytically investigates the stationary states of a simple PT-symmetric two-mode Bose-Einstein condensate model, revealing explicit eigenvalues and eigenstates that mirror complex numerical results and providing insights into nonlinear PT-symmetric quantum systems.

Contribution

It introduces an analytically solvable toy-model for a PT-symmetric BEC in a double well, offering explicit solutions and a linear matrix interpretation, advancing understanding of nonlinear PT-symmetric systems.

Findings

Explicit eigenvalues and eigenstates derived

Model solutions resemble numerical results for realistic potentials

A linear matrix model interpretation is provided

Abstract

The understanding of nonlinear PT-symmetric quantum systems, arising for example in the theory of Bose-Einstein condensates in PT-symmetric potentials, is widely based on numerical investigations, and little is known about generic features induced by the interplay of PT-symmetry and nonlinearity. To gain deeper insights it is important to have analytically solvable toy-models at hand. In the present paper the stationary states of a simple toy-model of a PT-symmetric system are investigated. The model can be interpreted as a simple description of a Bose-Einstein condensate in a PT-symmetric double well trap in a two-mode approximation. The eigenvalues and eigenstates of the system can be explicitly calculated in a straight forward manner; the resulting structures resemble those that have recently been found numerically for a more realistic PT-symmetric double delta potential. In addition, a continuation of the system is introduced that allows an interpretation in terms of a simple linear matrix model.