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 $\Omega_\perp$, $\Omega_z$. Our primary prediction is the upper-critical angular velocity, $\omega_{c2} (\delta,T)$, as a function of temperature $T$ and resonance detuning $\delta$, 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 $\Omega_z\ll\Omega_\perp$, 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 $\omega_{c2} \sim\Omega_\perp(1-\delta/\delta_c)^{1/2}$ near $\delta_c\approx 2\epsilon_{F} + \frac\gamma 2\epsilon_{F} \ln(\epsilon_F/\hbar\Omega_\perp)$ (with $\Delta$ the BCS gap and $\gamma$ resonance width), and extending bulk result $\hbar\omega_{c2} \approx 2\Delta^2/\epsilon_{F}$ to a finite number of atoms in a trap. In the BEC regime of $\delta < 0$ we find $\omega_{c2} \to\Omega^-_\perp$, where molecular superfluidity can only be destroyed by large quantum fluctuations associated with comparable boson and vortex densities.