Physical properties of the normal phase, ultracold Fermi gas at unitarity: Thermodynamics, universality, and beyond

Shizhong Zhang, Anthony J. Leggett

Marcus Bluhm, Jiaxun Hou, Thomas Schäfer

We determine the shear viscosity of the ultracold Fermi gas at unitarity in the normal phase using hydrodynamic expansion data. The analysis is based on a generalized fluid dynamic framework which ensures a smooth transition between the fluid dynamic core of the cloud and the ballistic corona. We use expansion data taken by Joseph, Elliott, and Thomas [Shear Viscosity of a Universal Fermi Gas Near the Superfluid Phase Transition, Phys. Rev. Lett. 115, 020401 (2015).PRLTAO0031-900710.1103/PhysRevLett.115.020401] and measurements of the equation of state by Ku et al. [Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas, Science 335, 563 (2012).SCIEAS0036-807510.1126/science.1214987]. We find that the shear viscosity to particle density ratio just above the critical temperature is η/n|_{T_{c}}=0.41±0.11. We also obtain evidence that the shear viscosity to entropy density ratio has a minimum slightly above T_{c} with η/s|_{min}=0.50±0.10.

D. K. Watson

The transition from the weakly interacting BCS regime to the strongly interacting unitary regime is explored for ultracold trapped Fermi gases assuming a normal mode description of the gas instead of the conventional Cooper pairing. The Pauli principle is applied ``on paper'' by using specific normal mode assignments. Energies, entropies, critical temperatures, and an excitation frequency are studied and compared to existing results in the literature. These normal modes have been derived analytically for N identical, confined particles from a first-order L=0 group theoretic solution of a three-dimensional Hamiltonian with a general two-body interaction. In previous studies, normal modes were able to describe the unitary regime obtaining ground state energies comparable to benchmark results and thermodynamics quantities in excellent agreement with experiment. In a recent study, the behavior of the normal mode frequencies was investigated for Hamiltonians with a range of interparticle interaction strengths from BCS to unitarity in the first test of this approach beyond the unitary regime, and a microscopic basis of the large excitation gaps and universal behavior at unitarity was proposed. Based on the success of these earlier studies, the current paper continues to explore the ability of normal modes to describe superfluidity along the BCS to unitarity transition. The results confirm earlier conclusions that the physics of superfluidity can be described using normal modes across a wide range of interparticle interaction strengths and offer an alternative to the two-body pairing models commonly used to describe superfluidity along this transition.

Erik M. Weiler, Theja N. De Silva

Edward Taylor, Hui Hu, Xia-Ji Liu +1 more

We present the results of a variational calculation of the frequencies of the low-lying Landau two-fluid hydrodynamic modes in a trapped Fermi superfluid gas at unitarity. Landau's two-fluid hydrodynamics is expected to be the correct theory of Fermi superfluids at finite temperatures close to unitarity, where strong interactions give rise to collisional hydrodynamics. Two-fluid hydrodynamics predicts the existence of in-phase modes in which the superfluid and normal fluid components oscillate together, as well as out-of-phase modes where the two components move against each other. We prove that, at unitarity, the dipole and breathing in-phase modes are locally isentropic. Their frequencies are independent of temperature and are the same above and below the superfluid transition, a feature due as much to the harmonic trapping potential as to the thermodynamic properties at unitarity. The out-of-phase modes, in contrast, are strongly dependent on temperature and hence can be used to test the thermodynamic properties and superfluid density of a Fermi gas at unitarity. We give numerical results for the frequencies of these modes as function of temperature in an isotropic trap at unitarity.

Selim Jochim