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 $^6$Li atoms near a Feshbach resonance. The measurements address the apparent discrepancy between the results of Kinast et al., [Phys. Rev. Lett. {\bf 92}, 150402 (2004)] and those of Bartenstein et al., [Phys. Rev. Lett. {\bf 92}, 203201 (2004)]. Over the range of magnetic field from 770 G to 910 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 G, the measured frequency begins to decrease below predictions. For fields near 1080 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 G.Comment: 4 pages, 2 figures, 1 table. Revised in response to referees' Comments. Published in PRA(R

Measurement of the Entropy and Critical Temperature of a Strongly Interacting Fermi Gas

We report a model-independent measurement of the entropy, energy, and critical temperature of a degenerate, strongly interacting Fermi gas of atoms. The total energy is determined from the mean square cloud size in the strongly interacting regime, where the gas exhibits universal behavior. The entropy is measured by sweeping a bias magnetic field to adiabatically tune the gas from the strongly interacting regime to a weakly interacting regime, where the entropy is known from the cloud size after the sweep. The dependence of the entropy on the total energy quantitatively tests predictions of the finite-temperature thermodynamics.Comment: 16 pages, 3 figure

Evidence for Superfluidity in a Resonantly Interacting Fermi Gas

We observe collective oscillations of a trapped, degenerate Fermi gas of $^6$Li atoms at a magnetic field just above a Feshbach resonance, where the two-body physics does not support a bound state. The gas exhibits a radial breathing mode at a frequency of 2837(05) Hz, in excellent agreement with the frequency of $\nu_H\equiv\sqrt{10\nu_x\nu_y/3}=2830(20)$ Hz predicted for a {\em hydrodynamic} Fermi gas with unitarity limited interactions. The measured damping times and frequencies are inconsistent with predictions for both the collisionless mean field regime and for collisional hydrodynamics. These observations provide the first evidence for superfluid hydrodynamics in a resonantly interacting Fermi gas.Comment: 5 pages, ReVTeX4, 2 eps figs. Resubmitted to PRL in response to referees' comments. Title and abstract changed. Corrected error in Table 1, atom numbers for 0.33 TF and 0.5 TF data were interchanged. Corrected typo in ref 3. Added new figure of damping time versus temperatur

Universal Quantum Viscosity in a Unitary Fermi Gas

A Fermi gas of atoms with resonant interactions is predicted to obey universal hydrodynamics, where the shear viscosity and other transport coefficients are universal functions of the density and temperature. At low temperatures, the viscosity has a universal quantum scale $\hbar n$ where $n$ is the density, while at high temperatures the natural scale is $p_T^3/\hbar^2$ where $p_T$ is the thermal momentum. We employ breathing mode damping to measure the shear viscosity at low temperature. At high temperature $T$, we employ anisotropic expansion of the cloud to find the viscosity, which exhibits precise $T^{3/2}$ scaling. In both experiments, universal hydrodynamic equations including friction and heating are used to extract the viscosity. We estimate the ratio of the shear viscosity to the entropy density and compare to that of a perfect fluid.Comment: 13 pages, 3 figure

Scaling Flows and Dissipation in the Dilute Fermi Gas at Unitarity

We describe recent attempts to extract the shear viscosity of the dilute Fermi gas at unitarity from experiments involving scaling flows. A scaling flow is a solution of the hydrodynamic equations that preserves the shape of the density distribution. The scaling flows that have been explored in the laboratory are the transverse expansion from a deformed trap ("elliptic flow"), the expansion from a rotating trap, and collective oscillations. We discuss advantages and disadvantages of the different experiments, and point to improvements of the theoretical analysis that are needed in order to achieve definitive results. A conservative bound based on the current data is that the minimum of the shear viscosity to entropy density ration is that eta/s is less or equal to 0.5 hbar/k_B.Comment: 32 pages, prepared for "BCS-BEC crossoverand the Unitary Fermi Gas", Lecture Notes in Physics, W. Zwerger (editor), Fig. 5 corrected, note added; final version, corrected typo in equ. 9

Acoustic attenuation probe for fermion superfluidity in ultracold atom gases

Dilute gas Bose-Einstein condensates (BEC's), currently used to cool fermionic atoms in atom traps, can also probe the superfluidity of these fermions. The damping rate of BEC-acoustic excitations (phonon modes), measured in the middle of the trap as a function of the phonon momentum, yields an unambiguous signature of BCS-like superfluidity, provides a measurement of the superfluid gap parameter and gives an estimate of the size of the Cooper-pairs in the BEC-BCS crossover regime. We also predict kinks in the momentum dependence of the damping rate which can reveal detailed information about the fermion quasi-particle dispersion relation.Comment: 4 pages, 2 figures. Revised versio