Interaction Range and Universality in the BCS-BEC Crossover of Spin-Orbit Coupled Fermi Gases

Davide Giambastiani

We explore the evolution of a cold quantum gas of interacting fermions crossing from a Bardeen-
Cooper-Schrieer (BCS) superuidity to a Bose-Einstein condensation (BEC) of molecular bosons in
the presence of a tunable-range interaction among the fermions and of an articial magnetic eld,
which can be used to simulate a pseudo spin-orbit coupling (SOC). We nd that the crossover is
aected by the competition between the longer-range interaction tending to correlate the system over
large distances and favoring the BCS-like state, and the SOC term tending instead to favor the BEC-
like state with formation of tightly bound molecules with small size. We then calculate the critical
temperature, chemical potential and condensate fraction in dierent regimes for the SOC strength
and the strength and range of the atomic interactions, nding that universal behavior sets in and
persists for weak spin-orbit interaction, when the crossover is described in terms of the correlation
length. We then argue that for larger values of the SOC universality can be restored by taking into
account the existence of SOC-driven bosonic molecules, on the BCS side. Our results can be relevant
in view of current experiment with cold atoms in optical cavities, where tunable-range eective atomic
interactions can be engineered.