Superfluid Transition in a Rotating Fermi Gas with Resonant Interactions

We study a rotating atomic Fermi gas near a narrow $s$-wave Feshbach resonance in a uniaxial trap with frequencies ${\Omega }_{\perp }$, ${\Omega }_z$. We predict the upper-critical angular velocity, ${\omega }_{c2}(\delta ,T)$, as a function of temperature $T$ and detuning $\delta$ across the BEC-BCS crossover. The suppression of superfluidity at ${\omega }_{c2}$ is distinct in the BCS and BEC regimes, with the former controlled by depairing and the latter by the dilution of bosonic molecules. At low $T$ and ${\Omega }_z\ll {\Omega }_{\perp }$, in the BCS and crossover regimes of $0\lesssim \delta \lesssim {\delta }_c$, ${\omega }_{c2}$ is implicitly given by $\hslash \sqrt{{\omega }_{c2}^2+{\Omega }_{\perp }^2}\approx 2\Delta \sqrt{\hslash {\Omega }_{\perp }/{ϵ}_F}$, vanishing as ${\omega }_{c2}\sim {\Omega }_{\perp }(1-\delta /{\delta }_c{)}^{1/2}$ near ${\delta }_c\approx 2{ϵ}_F+\frac{\gamma }{2}{ϵ}_F\ln ({ϵ}_F/\hslash {\Omega }_{\perp })$ (with $\Delta$ the BCS gap and $\gamma$ the resonance width), and extending the bulk result $\hslash {\omega }_{c2}\approx 2{\Delta }^2/{ϵ}_F$ to a trap. In the BEC regime of $\delta <0$ we find ${\omega }_{c2}\to {\Omega }_{\perp }^{-}$, where molecular superfluidity is destroyed only by large quantum fluctuations associated with comparable boson and vortex densities.