Condensate fraction of a resonant Fermi gas with spin-orbit coupling in three and two dimensions

We study the effects of laser-induced Rashba-like spin-orbit coupling along the Bardeen-Cooper-Schrieffer–Bose-Einstein condensate (BCS-BEC) crossover of a Feshbach resonance for a two-spin-component Fermi gas. We calculate the condensate fraction in three and two dimensions and find that this quantity characterizes the crossover better than other quantities, like the chemical potential or the pairing gap. By considering both the singlet and the triplet pairings, we calculate the condensate fraction and show that a large-enough spin-orbit interaction enhances the singlet condensate fraction in the BCS side while suppressing it on the BEC side.