Universal Quantum Viscosity in a Unitary Fermi Gas

Unitary Fermi gases, first observed in 2002, have been widely studied as they provide model systems for tabletop research on a variety of strongly coupled systems, including the high temperature superconductors, quark-gluon plasmas and neutron stars. A two component 6Li unitary Fermi gas is created through a collisional Feshbach resonance centered around 834G, using all-optical trapping and cooling methods. In the vicinity of the Feshbach resonance, the atoms are strongly interacting and exhibit universal behaviors, where the equilibrium thermodynamic properties and transport coefficients are universal functions of the density n and temperature T. Thus, unitary Fermi gases provide a paradigm to study nonperturbative many-body physics, which is of fundamental significance and field-crossing interests.;This dissertation reports the measurement of the quantum shear viscosity in a 6Li unitary Fermi gas, which is the first measurement of transport coefficients for unitary Fermi gases. Two hydrodynamic experiments are employed to measure the shear viscosity eta in different temperature regimes: the anisotropic expansion for the high temperature regime and the radial breathing mode for the low temperature regime. In order to consistently and quantitatively extract the shear viscosity from these two experiments, the hydrodynamic theory is utilized to derive the universal hydrodynamic equations, which include both friction force and heating arising from frictions. These equations are simplified and solved, considering the universal properties of unitary Fermi gases as well as the specific conditions for each experiment.;Using these universal hydrodynamic equations, shear viscosity is extracted from the anisotropic expansion conducted at high temperatures and the predicted eta ∝ T3/2 scaling is demonstrated. The demonstration of the high temperature scaling sets a benchmark for measuring viscosity at low temperatures.;For the low temperature breathing mode experiment, the shear viscosity is directly related to the damping rate of an oscillating cloud, through the same universal hydrodynamic equations. The raw data from the previously measured radial breathing experiments are carefully analyzed to extract the shear viscosity. The low temperature data join with the high temperature data smoothly, which presents the full measurement of the quantum shear viscosity from nearly the ground state to the two-body Boltzmann regime.;The possible effects of the bulk viscosity in the high temperature anisotropic expansion experiment is also studied and found to be consistent with the predicted vanishing bulk viscosity in the normal fluid phase at unitarity.;Using the measured shear viscosity eta and the previously measured entropy density s, the ratio of eta/s is estimated and therefore compared to a string theory limit, which conjectures eta/ s ≥ h/4pikB for any fluid and defines a perfect fluid when the equality is satisfied. It is found that eta/s, for a unitary Fermi gas at the normal-superfluid transition point, is about 5 times the string limit. This shows that our unitary Fermi gas exhibit nearly perfect fluidity at low temperatures.;In addition to the quantum shear viscosity measurement, consistent and accurate methods of calibrating the energy and temperature for unitary Fermi gases is also developed in this thesis. While the energy is calculated from the cloud dimensions by exploiting the virial theorem, the temperature is determined using different methods for different temperature regimes. At high temperatures, the second virial coefficient approximation is applied to the energy density, from which a variety of thermodynamic quantities, including the temperature, are derived. For the low temperatures, the previous calibration from the energy E and entropy S measurement is improved by using a better calculation on the entropy and adding more constraints at higher temperatures using the second virial approximation. A power law curve with discontinues heat capacity is then fitted to the E-S curve and the temperature is obtained using ∂E/∂ S. The energy and temperature calibrations developed in this dissertation are universal and therefore can be applied on other thermodynamic and hydrodynamic experiments at unitarity.