In particular, the stability region of the quasi-two dimensional topological superfluid phase is increased.
The effective Hamiltonian provides a proper description for a quasi-low dimensional Fermi gas with spin-orbit coupling. To study the impact of these excited modes of the trapping potentials, one needs to construct an effective Hamiltonian in the form of a two-channel model, where the dressed molecules in the closed channel consist of the conventional Feshbach molecules as well as the excited state’s occupation in the confined direction. By analyzing the two-body bound state, we find that the population of the excited states in the tightly-confined direction would be significant when the two-body binding energy becomes comparable to or exceeds the energy gap by confinement. We firstly solve a two-body problem for spin-orbit coupled Fermi gas confined in quasi-low dimensional trapping potential. To show the basic method of tackling such system, we present two examples of one- and two-dimensional fermi gas. We review recent progress on the spin-orbit coupled Fermi gas in low-dimensions. Finally, we point out the future important issues in this rapidly growing research field. The experimental schemes for achieving non-Abelian superfluid phases are given. In particular, we introduce how the non-Abelian Majorana modes emerge in the SO coupled superfluid phases which can be topologically nontrivial or trivial, for which a few fundamental theorems are presented and discussed. Furthermore, we discuss the realization of novel superfluid phases for SO coupled ultrocold fermions. The optical Raman lattices exhibit novel intrinsic symmetries, which enable the natural realization of topological phases belonging to different symmetry classes, with the topology being detectable through minimal measurement strategies. We show that the so-called optical Raman lattice schemes, which combine the creation of the conventional optical lattice and Raman lattice with topological stability, can provide minimal methods with high experimental feasibility to realize 1D to 3D SO couplings. A pedagogical introduction to the SO coupling for ultracold atoms and topological quantum phases is presented. Here we review the physics of the SO coupled quantum gases, focusing on the latest theoretical and experimental progresses of realizing SO couplings beyond one-dimension (1D), and the further investigation of novel topological quantum phases in such systems, including the topological insulating phases and topological superfluids. The past several years have witnessed important progresses in both theory and experiment in the study of SO coupling and novel quantum states for ultracold atoms. Readership: Graduate students, post-docs and researchers working in the field of cold atomic gases.Ĭold atoms with laser-induced spin-orbit (SO) interactions provide promising platforms to explore novel quantum physics, in particular the exotic topological phases, beyond natural conditions of solids. Dynamical Spin-Orbit Coupling in Cold Atoms Induced by Cavity Field (Chuanzhou Zhu, Lin Dong, and Han Pu).Spin-Orbit Coupling in Three-Component Bose Gases (Wei Han and Wei Zhang).Superfluid Properties of a Spin-Orbit Coupled Fermi Gas (Juan Yao, Shanshan Ding, Zhenhua Yu, and Shizhong Zhang).Pairing Superfluidity in Spin-Orbit Coupled Ultracold Fermi Gases (Xingze Qiu and Wei Yi).Rashba-Spin-Orbit Coupling in Interacting Fermi Gases (Jayantha P Vyasanakere).Quasi-Low Dimensional Fermi Gases with Spin-Orbit Coupling (Ren Zhang).Spin-Orbit Coupling and Topological Phases for Ultracold Atoms (Long Zhang and Xiong-Jun Liu).This is the first review volume dedicated to this active research frontier, and provides a comprehensive and pedagogical summary of recent progresses in the field.Ĭhapter 2: Quasi-low Dimensional Fermi Gases with Spin-orbit Coupling The intended audience corresponds to graduate students, post-docs and colleagues working in the field of cold atomic gases. This is a review volume covering a wide range of topics in this newly developed research field.