Fully gapped, spin singlet superconductors with antisymmetric spin-orbit coupling in a Zeeman magnetic field provide a promising route to realize superconducting states with non-Abelian topological order and therefore fault-tolerant quantum computation. In this talk, I will present non-perturbative numerical calculations using a quantum Monte Carlo dynamical cluster approximation to study the superconducting properties of a doped two-dimensional attractive Hubbard model with Rashba spin-orbit coupling in a Zeeman magnetic field. In particular, I will discuss how the Rashba coupling enhances the pairing correlations through a spin-flip driven enhancement of the amplitude for the propagation of a pair of electrons in time-reversed states. I will show that it can restore a finite temperature s-wave superconducting state in the presence of a pair-breaking Zeeman field and discuss the circumstances under which this superconducting state is expected to be topologically non-trivial.
