Measuring the Hydrodynamic Linear Response of a Unitary Fermi Gas

We directly observe the hydrodynamic linear response of a unitary Fermi gas confined in a box potential and subject to a spatially periodic optical potential that is translated into the cloud at speeds ranging from subsonic to supersonic. We show that the time-dependent change of the density profile is sensitive to the thermal conductivity, which controls the relaxation rate of the temperature gradients and hence the responses arising from adiabatic and isothermal compression.

Figure 1

A unitary Fermi gas, confined in a box, is driven by a moving spatially periodic potential. (a) The box potential is created by two 669 nm sheet beams (top and bottom) and four vertically propagating 532 nm sheet beams. (b) Column density. (c) Integrated column density in the box potential showing 1D profile.

Figure 2

Response to subsonic perturbations. Density change, $\delta n/n_0$, for a sinusoidal spatial perturbation with $\lambda =30\mu \mathrm{m}$, moving into the sample at a speed $v=\lambda f<c_0$ for 3 periods $1/f$. Data are shown as blue dots. Hydrodynamic model with $c_0=1.3\mathrm{cm}/\mathrm{s}$, $\delta U_0=0.26{\epsilon }_{F0}$, and $\epsilon =0.29$ (red curves) for frequencies (a) $f=200\mathrm{Hz}$, $v/c_0=0.46$, (b) $f=250\mathrm{Hz}$, $v/c_0=0.58$, (c) $f=300\mathrm{Hz}$, $v/c_0=0.69$, and (d) $f=350\mathrm{Hz}$, $v/c_0=0.81$.

Figure 3

Response to subsonic perturbations. Density change, $\delta n/n_0$, for a sinusoidal spatial perturbation with $\lambda =19\mu \mathrm{m}$, moving into the sample at a subsonic speed $v=\lambda f<c_0$ for 4 periods $1/f$. Data are shown as blue dots. Hydrodynamic model with $c_0=1.3\mathrm{cm}/\mathrm{s}$, $\delta U_0=0.22{\epsilon }_{F0}$, and $\epsilon =0.23$ (red curves) for frequencies (a) $f=300\mathrm{Hz}$, $v/c_0=0.44$, (b) $f=400\mathrm{Hz}$, $v/c_0=0.58$, (c) $f=500\mathrm{Hz}$, $v/c_0=0.73$, and (d)$f=600\mathrm{Hz}$, $v/c_0=0.88$.

Figure 4

Response to a supersonic perturbation. Density change, $\delta n/n_0$, for a sinusoidal spatial perturbation with $\lambda =19\mu \mathrm{m}$, moving into the sample at a supersonic speed $v=\lambda f=1.17c_0$ for 4 periods $1/f$ and $f=800\mathrm{Hz}$. Data are shown as blue dots. Hydrodynamic model with $c_0=1.3\mathrm{cm}/\mathrm{s}$, $\delta U_0=0.22{\epsilon }_{F0}$, and $\epsilon =0.23$ (red curve). The thermal conductivity ${\kappa }_T$ cannot be extracted from the fit of the model to the supersonic data.