Recent years have witnessed the considerable progresses in quantum simulation with spin-orbit coupled quantum gases. In the particular, the realization of 2D spin-orbit coupling for ultracold atoms in optical lattices opens up the quantum simulation for non-Abelian synthetic gauge fields. In this talk, following a pedagogic introduction to the spin-orbit coupling effects and ulracold atoms, I will discuss the recent progresses of the theoretical and experimental studies of topological quantum gases with 2D and 3D spin-orbit couplings. In particular, we focus the proposal and realization of 2D and 3D spin-orbit couplings with high controllability and long lifetime, with which several novel topological states, including the 3D Weyl semimetal with minimal number of Weyl points, become achievable in experiment. We further introduce the dynamical classification of topological quantum phases, with the theory being built on the so-called dynamical bulk-surface correspondence, which leads to the high-precision detection of topological phases. The application of the dynamical schemes to observing in experiment the high-dimensional topological phases in spin-orbit coupled systems is presented. We finally discuss the new developments and also future interesting issues in this promising field, including the realization of dynamical non-Abelian gauge fields in optical lattice, which may facilitate the study of a few outstanding problems in both theory and experiment.

**About the speaker:**

Xiong-Jun Liu received Ph.D in Texas A&M University in 2011, and was a postdoctoral fellow in University of Maryland (2011-2012), IAS HKUST and MIT (2012-2014). He joined the faculty of International Center for Quantum Materials at Peking University (09/2014), became tenured (07/2018), and now a full professor (from 01/2019). He works in condensed matter theory and ultracold atoms, focusing on quantum simulation and topological matter: topological superconductors, synthetic gauge fields, non-equilibrium topological quantum systems, and strongly correlated topological states. He received the National Science Fund for Distinguished Young Scholars (2018), and the AAPPS-APCTP CN Yang Award (2019).