Realizing PT-symmetric BEC subsystems in closed hermitian systems

TL;DR

This paper demonstrates how PT-symmetric Bose-Einstein condensate subsystems can be realized within closed hermitian systems, eliminating the need for external in- and outfluxes, and analyzes their properties using matrix and Gross-Pitaevskii models.

Contribution

It introduces a hermitian system embedding PT-symmetric subsystems, showing they retain PT-symmetry without external coupling, and compares simple and complex models for accurate descriptions.

Findings

Simple matrix model captures qualitative PT-symmetric properties.

Quantitative agreement achieved for sufficiently isolated wells.

Wave function phase difference conditions are identified for PT-symmetry.

Abstract

In open double-well Bose-Einstein condensate systems which balance in- and outfluxes of atoms and which are effectively described by a non-hermitian PT-symmetric Hamiltonian PT-symmetric states have been shown to exist. PT-symmetric states obey parity and time reversal symmetry. We tackle the question of how the in- and outfluxes can be realized and introduce a hermitian system in which two PT-symmetric subsystems are embedded. This system no longer requires an in- and outcoupling to and from the environment. We show that the subsystems still have PT-symmetric states. In addition we examine what degree of detail is necessary to correctly model the PT-symmetric properties and the bifurcation structure of such a system. We examine a four-mode matrix model and a system described by the full Gross-Pitaevskii equation in one dimension. We see that a simple matrix model correctly describes the qualitative properties of the system. For sufficiently isolated wells there is also quantitative agreement with the more advanced system descriptions. We also investigate which properties the wave functions of a system must fulfil to allow for PT-symmetric states. In particular the requirements for the phase difference between different parts of the system are examined.