Nambu-Goldstone mode in a rotating dilute Bose-Einstein condensate

The Nambu-Goldstone mode (NGM), associated with vortex nucleation in a harmonically confined, two-dimensional dilute Bose-Einstein condensate is studied. We argue, based on exact diagonalization calculations, that the NGM manifests in the lowest-lying envelope of the quasidegenerate spectrum that emerges as the vortex is about to enter the condensate. The quasidegenerate states constitute a series of octupole-mode branches that originate primarily from pairwise repulsive interactions between octupole excitations and are distinguished by the number of admixed quadrupolar excitations. As the vortex approaches the center of the condensate and the system's axisymmetry is restored, the NGM becomes massive due to its coupling to higher rotational bands. We clarify the mechanism of this mass acquisition by using a newly developed projection-operator method.