Collective excitation of a trapped Bose-Einstein condensate with spin-orbit coupling

摘要

We investigate the collective excitations of a Raman-induced spin-orbitcoupled Bose-Einstein condensate confined in a quasi one-dimension harmonictrap using the Bogoliubov method. By tuning the Raman coupling strength, threephases of the system can be identified. By calculating the transition strength,we are able to classify various excitation modes that are experimentallyrelevant. We show that the three quantum phases possess distinct features intheir collective excitation properties. In particular, the spin dipole and thespin breathing modes can be used to clearly map out the phase boundaries. Weconfirm these predictions by direct numerical simulations of the quenchdynamics that excites the relevant collective modes.