Excitation spectrum and instability of a two-species Bose-Einstein condensate

TL;DR

This paper numerically investigates the excitation spectrum and stability of a two-species Bose-Einstein condensate, revealing a phase transition marked by symmetry breaking and a zero-frequency excitation mode.

Contribution

It provides the first detailed numerical analysis of the excitation spectrum and instability leading to phase transitions in two-species Bose-Einstein condensates.

Findings

Ground state density becomes unstable in certain parameters

Phase transition to a symmetry-broken state occurs

Lowest excitation frequency approaches zero at transition

Abstract

We numerically calculate the density profile and excitation spectrum of a two-species Bose-Einstein condensate for the parameters of recent experiments. We find that the ground state density profile of this system becomes unstable in certain parameter regimes, which leads to a phase transition to a new stable state. This state displays spontaneously broken cylindrical symmetry. This behavior is reflected in the excitation spectrum: as we approach the phase transition point, the lowest excitation frequency goes to zero, indicating the onset of instability in the density profile. Following the phase transition, this frequency rises again.