Spin-orbit coupling and superfluidity in ultracold quantum gases

Considering BECs of $^{87}$Rb and $^{39}$K, we explore the effects of spin-orbit coupling on the superfluidity of this ultracold quantum gas. In particular, we are interested in the analogue of a spin-Hall effect in this system, where, effectively, two different spin states experience different magnetic fields. We study this system numerically using the Gross-Piteavskii equation, and find that various ``structures’’ emerge depending on the spin-orbit, trap, and interaction parameters, such as the formation of oppositely rotating vortices in the two different spin components, or stripes, or spin-domain formation. We discuss progress towards realizing this system with our BEC experiments in the laboratory.