Collective excitations of Bose-Einstein condensate in a synthetic magnetic field

The realization of synthetic magnetic field offers a new opportunity for the study of topological phenomena with ultracold neutral atoms. Synthetic magnetic field can also strongly modify the superfluid properties of a Bose-Einstein condensate by generating a rotational velocity field and creating vortices. We explore the collective excitations in a spin-orbit-coupled Bose-Einstein condensate in the presence of a position-dependent detuning or Raman coupling. We find that various collective modes such as the scissors mode, the quadrupole mode, and the dipole mode can be coupled together due to the rotational velocity field. We have developed a hydrodynamic theory for the description of the collective excitations in both the single-minimum phase and the plane-wave phase. Our theoretical results are also compared to the numerical simulation of the Gross-Pitaevskii equation.