Spin-orbit Coupling in Optical lattices

In this review, we discuss the physics of spin-orbit coupled quantum gases in optical lattices. After reviewing some relevant experimental techniques, we introduce the basic theoretical model and discuss some of its generic features. In particular, we concentrate on the interplay between spin-orbit coupling and strong interactions and show how it leads to various exotic quantum phases in both the Mott insulating and superfluid regimes. Phase transitions between the Mott and superfluid states are also discussed. Cold atom experiments are performed with charge-neutral atoms [1, 2]. At first sight, this would have precluded the effects of orbital magnetism, as well as spin-orbit coupling to be studied in these cold atomic gases. However, in the past few years, by using atom-light coupling (Raman lasers and shaking optical lattice), it has become possible to simulate these effects in neutral atomic sample. This provides cold ato