| Gauge fields and spin-orbit interactions, which are absent for neutral atoms, can be engineered by suitably coupling atoms with laser fields or by periodically shaking optical lattices. The experimental realization of synthetic gauge fields and spin-orbit coupling provides a versatile platform for the exploration of novel quantum phases in interacting atomic gases and for the simulation of condensed matter phenomena. In this dissertation, I will study the quantum phases and dynamics of ultracold atomic gases in harmonic traps or optical lattices in the presence of synthetic gauge fields and spin-orbit coupling. The topics in this dissertation include the collaborative experimental observation of Zitterbewegung oscillation, Dicke-type phase transition, and tunable spin-orbit coupling in spin-orbit coupled Bose-Einstein condensates, the theoretical investigation of Fulde-Ferrell-Larkin-Ovchinnikov states and topological superfluids with Majorana fermions in spin-orbit coupled degenerate Fermi gases, and the study of atomic gases in periodically driven optical lattices, etc. |
