Superfluid transition in a rotating resonantly-interacting Fermi gas

TL;DR

This paper predicts the critical rotation speed at which superfluidity breaks down in a rotating Fermi gas near a Feshbach resonance, revealing different mechanisms in BCS and BEC regimes and extending bulk results to trapped gases.

Contribution

It provides a detailed theoretical analysis of the upper-critical angular velocity in a rotating Fermi gas across the BEC-BCS crossover, including effects of trap geometry and resonance detuning.

Findings

Critical angular velocity depends on temperature and detuning.

Superfluid suppression mechanisms differ between BCS and BEC regimes.

Extension of bulk superfluidity results to finite trapped atom systems.

Abstract

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.