Finite-Temperature Collective Dynamics of a Fermi Gas in the BEC-BCS Crossover

We report on experimental studies on the collective behavior of a strongly interacting Fermi gas with tunable interactions and variable temperature. A scissors mode excitation in an elliptical trap is used to characterize the dynamics of the quantum gas in terms of hydrodynamic or near-collisionless behavior. We obtain a crossover phase diagram for collisional properties, showing a large region where a nonsuperfluid strongly interacting gas shows hydrodynamic behavior. In a narrow interaction regime on the BCS side of the crossover, we find a novel temperature-dependent damping peak, suggesting a relation to the superfluid phase transition.

Figure 1

(a) Schematic showing the excitation of the scissors mode. (1) The gas (shaded region) is at rest, in equilibrium with the trap (heavy solid line). (2) The trap is suddenly rotated. (3) The gas oscillates around the new equilibrium position. (b) Scissors mode oscillations observed at the lowest obtainable temperature ($T\approx 0.1T_F$ at 834 G) for various magnetic fields. On the left side, where $B=750$, 834, and 900 G ($1/k_{F}a=1.4$, 0.0, and $-0.6$), the gas is hydrodynamic. On the right side, where $B=661$, 970, and 1132 G ($1/k_{F}a=5.0$, $-1.0$, and $-1.44$), the gas is nearly collisionless and exhibits the characteristic two-frequency oscillation. Here, ${\omega }_x=2\pi \times 580\mathrm{Hz}$, ${\omega }_y=2\pi \times 270\mathrm{Hz}$, and $T_F=0.69\mu \mathrm{K}$.

Figure 2

Frequency and damping rate for the scissors mode oscillation for $B=895\mathrm{G}$ ($1/k_{F}a=-0.45$, solid squares) and at $B=834\mathrm{G}$ ($1/k_{F}a=0$, open circles). The frequency limits in the hydrodynamic and collisionless regimes are shown by the horizontal lines in (a), including small corrections for the anharmonicity of the trap [24]. The lines in (b) are introduced as guides to the eye. For $\tilde{T}$ greater than 1.14, the scissors mode oscillations are fit by a two-frequency cosine function (for details see text).

Figure 3

Low-temperature damping peak observed in a narrow magnetic-field region at the BCS side of the resonance ($1/k_{F}a\approx -0.5$). The solid lines are introduced as guides to the eye.

Figure 4

Phase diagram for the hydrodynamic behavior of the scissors mode in terms of (a) the temperature parameter $\tilde{T}$ and (b) the real temperature $T$. The smooth transition from hydrodynamic to collisionless is characterized by the temperature parameter ${\tilde{T}}_H$ (temperature $T_H$). The second damping peak near $1/k_{F}a\approx -0.5$ is marked by ${\tilde{T}}_S$ ($T_S$). In (a) the hatched region indicates the region ($\tilde{T}<0.1$) where our thermometry does not produce reliable results. In (b) the solid line shows a theoretical curve for the phase transition to superfluidity [25].