Exploring scale invariance in the expansion of a spherical unitary Fermi gas

Abstract

A unitary Fermi gas in an isotropic harmonic trap is predicted to show scale and conformal symmetry that have important consequences in its thermodynamic and dynamical properties. By experimentally realizing an isotropic harmonic trap, we study the expansion of a unitary Fermi gas and demonstrate its universal expansion dynamics along different directions and at different temperatures. We show that as a consequence of SO(2,1) symmetry, the measured release energy is equal to that of the trapping energy. In addition, away from resonance when scale invariance is broken, we determine the effective exponent $\gamma$ that relates the chemical potential and average density along the BEC-BCS crossover, which qualitatively agrees with the mean field predictions. This work opens the possibility of studying non-equilibrium dynamics in a conformal invariant system in the future.Comment: 15 pages and 8 figur