Spin-orbit (SO) coupling is a fundamental quantum effect, and has played an essential role in a number of prominent quantum phenomena. Recently, there has been considerable interest in emulating SO effects and topological phases with ultracold atoms. Here I will present the recent theoretical and experimental progresses in the quantum simulation of synthetic SO coupling and topological phase for ultracold atoms. After a brief introduction to the background, I will turn to our recent theoretical proposal and experimental realization of 2D SO coupling and topological bands in an optical Raman lattice . Based on the current realization, I will further introduce how to engineer a 2D Dirac semimetal driven by a new type of 2D SO coupling, and propose to observe a chiral Fulde-Ferrell superfluid . In this study, I will also show a fundamental theorem that the topology of chiral superfluids can be uniquely determined from the unpaired normal states. This generic theorem is also useful for condensed matter physics and material science in search for new topological superconductors. The interesting issues for the next study will also be discussed.
Z. Wu, L. Zhang, W. Sun, X. Xu, B. Wang, Y. Deng, S. Chen, X. -J. Liu and J. -W. Pan, Science, 354, 88 (2016).
T. -F. Jeffrey Poon and X. -J. Liu, arXiv:1701.01992v2.