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 $Omega_zllOmega_perp$, in the BCS and crossover regimes of $0 lesssim delta lesssim delta_c$, $omega_{c2}$ is implicitly given by $hbar sqrt{omega_{c2}^2 +Omega_perp^2}approx 2Delta sqrt{hbar Omega_perp/epsilon_F}$, vanishing as $omega_{c2} simOmega_perp(1-delta/delta_c)^{1/2}$ near $delta_capprox 2epsilon_{F} + fracgamma 2epsilon_{F} ln(epsilon_F/hbarOmega_perp)$ (with $Delta$ the BCS gap and $gamma$ resonance width), and extending bulk result $hbaromega_{c2} approx 2Delta^2/epsilon_{F}$ to a finite number of atoms in a trap. In the BEC regime of $delta < 0$ we find $omega_{c2} toOmega^-_perp$, where molecular superfluidity can only be destroyed by large quantum fluctuations associated with comparable boson and vortex densities.