Superfluid Transition in a Rotating Fermi Gas with Resonant Interactions

Abstract

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