Breakdown of hydrodynamics in the radial breathing mode of a strongly interacting Fermi gas

We measure the magnetic-field dependence of the frequency and damping time for the radial breathing mode of an optically trapped Fermi gas of ${}^6\mathrm{Li}$ atoms near a Feshbach resonance. The measurements address the apparent discrepancy between the results of Kinast et al. [Phys. Rev. Lett. 92, 150402 (2004)] and those of Bartenstein et al. [Phys. Rev. Lett. 92, 203201 (2004)]. Over the range of magnetic field from $770\text{to}910\mathrm{G}$, the measurements confirm the results of Kinast et al. Close to resonance, the measured frequencies are in excellent agreement with predictions for a unitary hydrodynamic gas. At a field of $925\mathrm{G}$, the measured frequency begins to decrease below predictions. For fields near $1080\mathrm{G}$, we observe a breakdown of hydrodynamic behavior, which is manifested by a sharp increase in frequency and damping rate. The observed breakdown is in qualitative agreement with the sharp transition observed by Bartenstein et al. at $910\mathrm{G}$.

Figure 1

Magnetic-field dependence of the frequency $\omega$ of the radial breathing mode. The solid line is the theory based on superfluid hydrodynamics from Hu et al. [17]. The dashed line is the hydrodynamic frequency for a unitarity gas, $\sqrt{10∕3}$, as predicted at resonance. Note that the top (magnetic-field) axis is not linear.

Figure 2

Magnetic-field dependence of the damping rate $1∕\tau$ of the radial breathing mode. Damping rate (solid circles, axis labeled on the right-hand side); frequency (data—open circles, theory—solid curve, axis labeled on the left-hand side); solid curve (predicted frequency). The maximum damping ratio occurs at $1080\mathrm{G}$ and exceeds the maximum 0.09 permitted for collisional dynamics by a factor of 2. Note that the top (magnetic-field) axis is not linear.