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 $Ω_\perp$, $Ω_z$. Our primary prediction is the upper-critical angular velocity, $ω_{c2} (δ,T)$, as a function of temperature $T$ and resonance detuning $δ$, ranging across the BEC-BCS crossover. The rotation-driven suppression of superfluidity at $ω_{c2}$ 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 $Ω_z\llΩ_\perp$, in the BCS and crossover regimes of $0 \lesssim δ\lesssim δ_c$, $ω_{c2}$ is implicitly given by $\hbar \sqrt{ω_{c2}^2 +Ω_\perp^2}\approx 2Δ\sqrt{\hbar Ω_\perp/ε_F}$, vanishing as $ω_{c2} \simΩ_\perp(1-δ/δ_c)^{1/2}$ near $δ_c\approx 2ε_{F} + \fracγ2ε_{F} \ln(ε_F/\hbarΩ_\perp)$ (with $Δ$ the BCS gap and $γ$ resonance width), and extending bulk result $\hbarω_{c2} \approx 2Δ^2/ε_{F}$ to a finite number of atoms in a trap. In the BEC regime of $δ< 0$ we find $ω_{c2} \toΩ^-_\perp$, where molecular superfluidity can only be destroyed by large quantum fluctuations associated with comparable boson and vortex densities.