Superfluid transition in a rotating resonantly-interacting Fermi gas

We study a rotating atomic Fermi gas near a narrow s-wave Feshbach resonance in a uniaxial harmonic trap with frequencies ${\mathrm{\Omega }}_{\perp }$, ${\mathrm{\Omega }}_z$. Our primary prediction is the upper-critical angular velocity, $\omega_{c2} (\delta,T)$,asafunctionoftemperature$T$andresonancedetuning$\delta$, ranging across the BEC-BCS crossover. The rotation-driven suppression of superfluidity at ${\omega }_{c2}$ is quite distinct in the BCS and BEC regimes, with the former controlled by Cooper-pair depairing and the latter by the dilution of bosonic molecules. At low $T$ and ${\mathrm{\Omega }}_z\ll {\mathrm{\Omega }}_{\perp }$, in the BCS and crossover regimes of $0\lesssim \delta \lesssim {\delta }_c$, ${\omega }_{c2}$ is implicitly given by $\hbar \sqrt{\omega_{c2}^2 +\Omega_\perp^2}\approx 2\Delta \sqrt{\hbar \Omega_\perp/\epsilon_F}$, vanishing as ${\omega }_{c2}\sim {\mathrm{\Omega }}_{\perp }(1-\delta \mathrm{/}{\delta }_c{)}^{1\mathrm{/}2}$ near $\delta_c\approx 2\epsilon_{F} + \frac\gamma 2\epsilon_{F} \ln(\epsilon_F/\hbar\Omega_\perp)$(with$\Delta$theBCSgapand$\gamma$resonancewidth),andextendingbulkresult$\hbar\omega_{c2} \approx 2\Delta^2/\epsilon_{F}$ to a finite number of atoms in a trap. In the BEC regime of $\delta <0$ we find ${\omega }_{c2}\to {\mathrm{\Omega }}_{\perp }^{-}$, where molecular superfluidity can only be destroyed by large quantum fluctuations associated with comparable boson and vortex densities.