Verification of exceptional points in the collapse dynamics of Bose-Einstein condensates

TL;DR

This paper investigates how exceptional points influence the collapse dynamics of Bose-Einstein condensates and proposes a harmonic inversion method to experimentally verify their presence.

Contribution

It introduces a novel harmonic inversion analysis technique to detect exceptional points in BEC collapse dynamics, bridging numerical signatures and experimental verification.

Findings

Exceptional points cause coalescence of states at bifurcation.

Harmonic inversion of collapse signals reveals exceptional point signatures.

Method enables experimental detection of exceptional points in BECs.

Abstract

In Bose-Einstein condensates with an attractive contact interaction the stable ground state and an unstable excited state emerge in a tangent bifurcation at a critical value of the scattering length. At the bifurcation point both the energies and the wave functions of the two states coalesce, which is the characteristic of an exceptional point. In numerical simulations signatures of the exceptional point can be observed by encircling the bifurcation point in the complex extended space of the scattering length, however, this method cannot be applied in an experiment. Here we show in which way the exceptional point effects the collapse dynamics of the Bose-Einstein condensate. The harmonic inversion analysis of the time signal given as the spatial extension of the collapsing condensate wave function can provide clear evidence for the existence of an exceptional point. This method can be used for an experimental verification of exceptional points in Bose-Einstein condensates.