Discovery of exceptional points in the Bose-Einstein condensation of gases with attractive 1/r-interaction

TL;DR

This paper investigates the bifurcation point in Bose-Einstein condensates with attractive 1/r-interaction, revealing it as an exceptional point with complex wave solutions indicating condensate decay.

Contribution

It demonstrates that the tangent bifurcation in the extended Gross-Pitaevskii equation corresponds to an exceptional point, linking nonlinear bifurcation phenomena with linear non-Hermitian physics.

Findings

Identification of the bifurcation as an exceptional point

Complex wave solutions indicating condensate decay

Analytic continuation reveals decay mechanisms at negative scattering lengths

Abstract

The extended Gross-Pitaevskii equation for the Bose-Einstein condensation of gases with attractive 1/r-interaction has a second solution which is born together with the ground state in a tangent bifurcation. At the bifurcation point both states coalesce, i.e., the energies and the wave functions are identical. We investigate the bifurcation point in the context of exceptional points, a phenomenon known for linear non-Hermitian Hamiltonians. We point out that the mean field energy, the chemical potential, and the wave functions show the same behavior as an exceptional point in a linear, non-symmetric system. The analysis of the analytically continued Gross-Pitaevskii equation reveals complex waves at negative scattering lengths below the tangent bifurcation. These solutions are interpreted as a decay of the condensate caused by an absorbing potential.