We discuss collective excitations of a trapped dilute Fermi gas within a hydrodynamic approximation. Analytical results are derived for both high- and low-temperature limits and are applied to
40K and
6Li systems of current experimental interest. We identify spectral signatures which can be used to detect the onset of Fermi degeneracy. Also, we find an interesting class of internal excitations with an unusual spectrum. Some of our results are relevant to the case of trapped bosons as well. Our analysis suggests several experiments which address fundamental problems of collective motion in quantum fluids.
In summary, we use all-optical methods with evaporative cooling near a Feshbach resonance to produce a strongly interacting degenerate Fermi gas. We observe hydrodynamic behavior in the expansion dynamics. At low temperatures, collisions may not explain the expansion dynamics. We observe hydrodynamics in the trapped gas. Our observations include collisionally-damped excitation spectra at high temperature which were not discussed above. In addition, we observe weakly damped breathing modes at low temperature. The observed temperature dependence of the damping time and hydrodynamic frequency are not consistent with collisional dynamics nor with collisionless mean field interactions. These observations constitute the first evidence for superfluid hydrodynamics in a Fermi gas.