Bifurcations and exceptional points in a PT-symmetric dipolar Bose-Einstein condensate

TL;DR

This paper explores the complex bifurcation structure and exceptional points in a PT-symmetric dipolar Bose-Einstein condensate using an innovative analytical continuation method involving bicomplex numbers.

Contribution

It introduces a novel analytical continuation technique for the Gross-Pitaevskii equation with dipolar interactions, revealing richer bifurcation scenarios and higher-order exceptional points.

Findings

Discovery of a fifth-order exceptional point.

Identification of a more complex bifurcation structure due to dipolar interactions.

Explanation of hidden property changes at bifurcation points.

Abstract

We investigate the bifurcation structure of stationary states in a dipolar Bose-Einstein condensate located in an external PT-symmetric potential. The imaginary part of this external potential allows for the effective description of in- and out-coupling of particles. To unveil the complete bifurcation structure and the properties of the exceptional points we perform an analytical continuation of the Gross-Pitaevskii equation, which is used to describe the system. We use an elegant and numerically efficient method for the analytical continuation of the Gross-Pitaevskii equation with dipolar interactions containing bicomplex numbers. The Bose-Einstein condensate with dipole interaction shows a much richer bifurcation scenario than a condensate without long-range interactions. The inclusion of analytically continued states can also explain property changes of bifurcation points which were hidden before, and allows for the examination of the properties of the exceptional points associated with the branch points. With the new analytically continued states we are able to prove the existence of an exceptional point of fifth order.