Yu-Ju Lin, Karina K. Jimenez Garcia, Ian B. Spielman
Spin-orbit (SO) coupling -- the interaction between a quantum particle's spin and its momentum -- is ubiquitous in nature, from atoms to solids. In condensed matter systems, SO coupling is crucial for the spin-Hall effect and topological insulators; it contributes to the electronic properties of materials such as GaAs, and is important for spintronic devices. Ultracold atoms, quantum many-body systems under nearly precise experimental control, would seem to be an ideal platform to study these fascinating SO coupled systems. While an atom's intrinsic SO coupling affects its electronic structure, it does not lead to coupling between the spin and the center- of-mass motion of the atom. Here, we engineer SO coupling (an equal sum of Rashba and Dresselhaus) in a neutral atomic Bose-Einstein condensate by dressing two atomic spin states with a pair of lasers. Not only is this the first SO coupling realized in ultracold atomic gases, it is also the first ever observed for bosons. Furthermore, in the presence of the optical coupling the interactions between the two dressed atomic spin states are modified, and we observe a quantum phase transition from a spatially spin-mixed state (lasers off) to a phase separated state (above a critical laser intensity). The location of this transition is in agreement with our theory and this technique -- equally applicable for bosons and fermions -- sets the stage to realize topological insulators in fermionic neutral atom systems.