Collective oscillations of a Fermi gas in the unitarity limit: Temperature effects and the role of pair correlations

We present detailed measurements of the frequency and damping of three different collective modes in an ultracold trapped Fermi gas of ${}^6\mathrm{Li}$ atoms with resonantly tuned interactions. The measurements are carried out over a wide range of temperatures. We focus on the unitarity limit, where the scattering length is much greater than all other relevant length scales. The results are compared to theoretical calculations that take into account Pauli blocking and pair correlations in the normal state above the critical temperature for superfluidity. We show that these two effects nearly compensate each other and the behavior of the gas is close to that of a classical gas.

Figure 1

(Color online) Sketch of the three collective modes investigated in this work: the compression mode, the quadrupole mode, and the scissors mode (from left to right). The oscillations take place in the plane of tight confinement, perpendicular to the direction of the elongated, cigar-shaped cloud. While the compression mode represents an oscillation of the overall cloud volume, the other two modes involve only surface deformations. Excitation of the quadrupole mode leads to an oscillating elliptic shape. The scissors mode appears as an angular oscillation of an elliptic cloud about a principal axis of an elliptic trap.

Figure 2

(Color online) Sloshing mode frequency ${\omega }_s$ normalized by the trap frequency ${\omega }_x$ as a function of temperature. The measured frequency shows a decrease with increasing temperature (dots), which is due to the increase in the size of the cloud. The lines show the expected frequency from a first-order anharmonic correction; see Appendix . To determine the cloud size for different temperatures we assume a harmonic potential (solid line) and a Gaussian potential (dashed line), respectively [15].

Figure 3

(Color online) Effective collision rate for a gas in the unitarity limit. The dashed curve is the classical result, the dashed-dotted includes Pauli blocking, and the solid line includes pairing correlations in the scattering matrix. The superfluid region for $T<T_c$ is indicated.

Figure 4

(Color online) Observed normalized mode frequencies versus temperature for the quadrupole mode, the scissors mode, and the compression mode. The error bars indicate the statistical error of a single frequency measurement. The full lines are the result of the theory for the normal state described in Sec. 3, which includes the combined effects of Pauli blocking and pair correlations; note that these curves start at $T=0.3T_F$, which in the ladder approximation used here is the transition temperature to the superfluid state. For illustrative purposes we also show the theoretical results when only Pauli blocking is taken into account (dashed-dotted lines) and those for a classical gas (dashed lines).

Figure 5

(Color online) Normalized mode damping versus temperature for the quadrupole mode, the scissors mode, and the compression mode. The points are experimental values, while the full lines represent our calculated values, taking into account both Pauli blocking and pairing effects. The dashed-dotted line takes only Pauli blocking into account, while the dashed line is the classical (high-temperature) result.

Figure 6

(Color online) Normalized mode damping versus normalized frequency for the quadrupole and scissors modes. The solid line shows the expected behavior for a harmonic trap. The arrows point toward the direction of increasing temperature.