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

We numerically calculate the zero-temperature 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.