We derive general conditions for the emergence of singlet Feshbach molecules in the presence of artificial Zeeman fields for arbitrary mixtures of Rashba and Dresselhaus spin-orbit coupling in two or three dimensions. We focus on the formation of two-particle bound states resulting from interactions between ultracold
spin-1/2 fermions, under the assumption that interactions are short ranged and occur only in the
s-wave channel. In this case, we calculate explicitly binding energies of Feshbach molecules and bound-state energy thresholds and analyze their dependence on spin-orbit couplings, Zeeman fields, interactions, and center-of-mass momentum, paying particular attention to the experimentally relevant case of spin-orbit couplings with equal Rashba and Dresselhaus (ERD) amplitudes.
Main purpose of this thesis is to present a discussion of the effects \nof artificial spin-orbit coupling and Zeeman fields in fermionic \nultra-cold atoms. Part of the work described here is inspired by \nthe experimental realization of artificial spin-orbit coupling (SOC) in the \nfermionic isotope
40K using a Raman technique, which was done by NIST group recently. The first aspect investigated is the formation of \ntwo-body bound states of fermions when artificial spin-orbit \ncoupling and artificial Zeeman fields are present. These bound-states \nare analyzed for two-hyperfine-state fermions in free space and \nin a harmonically confining potential. The second aspect explored \nis the study of spectroscopic and thermodynamic properties of \nthree-hyperfine-state fermions. These properties are investigated \nas a function of spin-orbit coupling and Zeeman fields for non-interacting \natoms, but when atom-atom interactions are also included, the many-body \nsystem consisting of three-hyperfine-state fermions \ncan exhibit exotic superfluid phases.
Triplet character of 2D-fermion dimers arising from
s-wave attraction via spin-orbit coupling and Zeeman splitting
We theoretically study spin-1/2 fermions confined to two spatial dimensions and experiencing isotropic short-range attraction in the presence of both spin-orbit coupling and Zeeman spin splitting -- a prototypical system for developing topological superfluidity in the many-body sector. Exact solutions for two-particle bound states are found to have a triplet contribution that dominates over the singlet part in an extended region of parameter space where the combined Zeeman- and center-of-mass-motion-induced spin-splitting energy is large. The triplet character of dimers is purest in the regime of weak s-wave interaction strength. Center-of-mass momentum is one of the parameters determining the existence of bound states, which we map out for both two- and one-dimensional types of spin-orbit coupling. Distinctive features emerging in the orbital part of the bound-state wave function, including but not limited to its p-wave character, provide observable signatures of unconventional pairing.