  An effective spin-orbit coupling can be generated in cold atom system by
engineering atom-light interactions. In this letter we study spin-1/2 and
spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that
the condensate wave function will develop non-trivial structures. From
numerical simulation we have identified two different phases. In one phase the
ground state is a single plane wave, and often we find the system splits into
domains and an array of vortices plays the role as domain wall. In this phase,
time-reversal symmetry is broken. In the other phase the condensate wave
function is a standing wave and it forms spin stripe. The transition between
them is driven by interactions between bosons. We also provide an analytical
understanding of these results and determines the transition point between the
two phases.
