Measurement of Sound Velocity in a Fermi Gas near a Feshbach Resonance

Sound waves are excited in an optically trapped degenerate Fermi gas of spin-up and spin-down atoms with magnetically tunable interactions. Measurements are made throughout the crossover region, from a weakly interacting Fermi gas through the resonant Fermi superfluid regime to a Bose condensate of dimer molecules. The measured sound velocities test theories of hydrodynamic wave propagation and predictions of the equation of state. At resonance, the sound velocity exhibits universal scaling with the Fermi velocity, to within 1.8% over a factor of 30 in density.

Figure 1

Sound propagation at the Feshbach resonance: (Top) 2D density profile showing initial perturbation. (Bottom) Gray (red) solid curve: Axial density profiles of the cloud for different in-trap propagation times; black dashed curve: valleys (inverted).

Figure 2

Normalized sound velocity $c_0/v_F$ versus the interaction parameter, $1/k_{F}a$. Black dotted curve: mean-field theory based on the Leggett ground state [33]. Gray (red) solid curve: quantum Monte Carlo calculation [33]. Black dashed curve: Thomas-Fermi theory of a molecular BEC, using $a_{\mathrm{mol}}=0.6a$. Closed and open circles represent trap depths 140–500 nK and 0.6–$80\mu \mathrm{K}$, respectively.

Figure 3

Axial positions $z$ of the left- and right-traveling density features of Fig. 1 versus the in-trap propagation time. Coordinates of the valleys [closed (blue) circles] and front peaks [open (red) circles] are shown. Dashed lines correspond to the measured Fermi radii ($z=\pm R_z$).

Figure 4

Valley [light gray (red) closed circles], peak [dark gray (blue) closed circles], and mean [open (green) circles] velocity versus excitation potential normalized to the global chemical potential. Measured at the Feshbach resonance.

Figure 5

Local sound velocity at the Feshbach resonance versus transverse coordinate $x$, showing a flat wave front. $x$ is given in units of the Thomas-Fermi radius. Images were divided into 21 longitudinal segments of equal transverse width. For the $i$th segment, $c_i(z=0)$ is measured. The dashed curve represents the line of site averaged isotropic sound speed, showing curved wave front.