Theoretical aspects of ultra-cold fermions in the presence of artificial spin-orbit coupling

Abstract

Main purpose of this thesis is to present a discussion of the effects of artificial spin-orbit coupling and Zeeman fields in fermionic ultra-cold atoms. Part of the work described here is inspired by the experimental realization of artificial spin-orbit coupling (SOC) in the fermionic isotope $^{40}$K using a Raman technique, which was done by NIST group recently. The first aspect investigated is the formation of two-body bound states of fermions when artificial spin-orbit coupling and artificial Zeeman fields are present. These bound-states are analyzed for two-hyperfine-state fermions in free space and in a harmonically confining potential. The second aspect explored is the study of spectroscopic and thermodynamic properties of three-hyperfine-state fermions. These properties are investigated as a function of spin-orbit coupling and Zeeman fields for non-interacting atoms, but when atom-atom interactions are also included, the many-body system consisting of three-hyperfine-state fermions can exhibit exotic superfluid phases.