Spin-orbit-coupling–induced anharmonic collective modes in a Bose-Einstein condensate

Abstract

The collective excitations of a spin-orbit–coupled Bose-Einstein condensate are investigated by using a variational method and numerical simulation. The collective modes are depicted in zero-momentum and plane-wave phases, while the mechanism for inducing the anharmonic collective oscillations is revealed analytically. The coupling among spin-orbit coupling, Raman coupling, and atomic interaction results in multiple external collective modes, which can lead to the collective dynamics being the superposition of the multiple harmonic oscillations. When one of the external frequencies is close to the inherent frequency of the conventional condensate and the amplitudes of other external frequencies vanish, the collective oscillations are harmonic, otherwise the collective oscillations are anharmonic. Thus the collective dynamics can undergo a harmonicity-anharmonicity transition. This can provide a possible way for elaborating distinct collective oscillation modes. Moreover, the collective excitations exhibit distinct properties in different phases, while the softening of collective modes is detected at the phase transition point, which can be used to map out the phase boundaries in experiment.