Measurement of the Entropy and Critical Temperature of a Strongly Interacting Fermi Gas

We report a model-independent measurement of the entropy, energy, and critical temperature of a degenerate, strongly interacting Fermi gas of atoms. The total energy is determined from the mean square cloud size in the strongly interacting regime, where the gas exhibits universal behavior. The entropy is measured by sweeping a bias magnetic field to adiabatically tune the gas from the strongly interacting regime to a weakly interacting regime, where the entropy is known from the cloud size after the sweep. The dependence of the entropy on the total energy quantitatively tests predictions of the finite-temperature thermodynamics.

Figure 1

Ratio of the mean square cloud size at 1200 G, $⟨z^2{⟩}_{1200}$, to that at 840 G, $⟨z^2{⟩}_{840}$, for an isentropic magnetic field sweep. $E_{840}$ is the total energy per particle of the strongly interacting gas at 840 G and $E_F$ is the ideal gas Fermi energy. The ratio converges to unity at high energy, as expected (dashed red line).

Figure 2

Measured entropy per particle of a strongly interacting Fermi gas at 840 G vs its total energy per particle (blue dots). Lower orange dot-dashed curve—ideal gas entropy $S_I(E_I)$; green dashes—pseudogap theory [21]; red dots—quantum Monte Carlo prediction [27]. Inset—entropy vs energy data showing a change in behavior at $E_c=0.94E_F$.