Density profiles and collective modes of a Bose-Einstein condensate with light-induced spin-orbit coupling

The phases of a Bose-Einstein condensate (BEC) with light-induced spin-orbit coupling (SOC) are studied within the mean-field approximation. The mixed BEC phase, in which the system condenses in a superposition of two plane wave states, is found to be stable for sufficiently small light-atom coupling, becoming unstable in a continuous fashion with increasing light-atom coupling. The structure of the phase diagram at fixed chemical potential for bosons with SOC is shown to imply an unusual density dependence for a trapped mixed BEC phase, with the density of one dressed spin state increasing with increasing radius, providing a unique experimental signature of this state. The collective Bogoliubov sound mode is shown to also provide a signature of the mixed BEC state, vanishing as the boundary to the regime of phase separation is approached.