Virial Theorem and Universality in a Unitary Fermi Gas

Unitary Fermi gases, where the scattering length is large compared to the interparticle spacing, can have universal properties, which are independent of the details of the interparticle interactions when the range of the scattering potential is negligible. We prepare an optically trapped, unitary Fermi gas of ${}^6\mathrm{Li}$, tuned just above the center of a broad Feshbach resonance. In agreement with the universal hypothesis, we observe that this strongly interacting many-body system obeys the virial theorem for an ideal gas over a wide range of temperatures. Based on this result, we suggest a simple volume thermometry method for unitary gases. We also show that the observed breathing mode frequency, which is close to the unitary hydrodynamic value over a wide range of temperature, is consistent with a universal hydrodynamic gas with nearly isentropic dynamics.

Figure 1

Verifying the virial theorem in a unitary Fermi gas of ${}^6\mathrm{Li}$: $⟨x^2⟩/⟨x^2(0)⟩$ versus $E/E_0$ showing linear scaling. Here $⟨x^2⟩$ is the measured transverse mean square size. $E$ is the total energy, calculated as in Ref. 13. $E_0$ and $⟨x^2(0)⟩$ denote ground state values.

Figure 2

Radial breathing frequency $\omega /{\omega }_{\perp }$ versus empirical temperature $\tilde{T}$ for a unitary gas of ${}^6\mathrm{Li}$ from Ref. 19, showing small variation. Open circles: Measured frequencies. Solid dots: Data after correction for anharmonicity. Lower dot-dashed line: Unitary hydrodynamic frequency, $\omega /{\omega }_{\perp }=1.84$. Upper dashed line: Noninteracting gas frequency $2{\omega }_x/{\omega }_{\perp }=2.10$.