Spectral singularities in PT-symmetric Bose-Einstein condensates

TL;DR

This paper investigates spectral singularities in PT-symmetric Bose-Einstein condensates, revealing new branch points and exceptional points through analytic continuation and matrix modeling, enhancing understanding of non-Hermitian quantum systems.

Contribution

It introduces an analytic continuation method for the nonlinear term in the Gross-Pitaevskii equation, uncovering new spectral branch points and exceptional points in PT-symmetric BECs.

Findings

Identification of new branch points where three levels coalesce

Demonstration of second and third order exceptional points

Validation of numerical results with a matrix model

Abstract

We consider the model of a PT-symmetric Bose-Einstein condensate in a delta-functions double-well potential. We demonstrate that analytic continuation of the primarily non-analytic term |psi|^2 psi - occurring in the underlying Gross-Pitaevskii equation - yields new branch points where three levels coalesce. We show numerically that the new branch points exhibit the behaviour of exceptional points of second and third order. A matrix model which confirms the numerical findings in analytic terms is given.