Universal Quantum Viscosity in a Unitary Fermi Gas

Abstract

<p>Unitary Fermi gases, first observed in 2002, have been widely</p><p>studied as they provide model systems for tabletop research on a</p><p>variety of strongly coupled systems, including the high temperature</p><p>superconductors, quark-gluon plasmas and neutron stars. A two</p><p>component $^6$Li unitary Fermi gas is created through a colliosnal</p><p>Feshbach resonance centered around $834$G, using all-optical</p><p>trapping and cooling methods. In the vicinity of the Feshbach</p><p>resonance, the atoms are strongly interacting and exhibit universal</p><p>behaviors, where the equilibrium thermodynamic properties and</p><p>transport coefficients are universal functions of the density $n$</p><p>and temperature $T$. Thus, unitary Fermi gases provide a paradigm to</p><p>study nonperturbative many-body physics, which is of fundamental</p><p>significance and field-crossing interests.</p><p>This dissertation reports the measurement of the quantum shear</p><p>viscosity in a $^6$Li unitary Fermi gas, which is the first</p><p>measurement of transport coefficients for unitary Fermi gases. Two</p><p>hydrodynamic experiments are employed to measure the shear viscosity</p><p>$\eta$ in different temperature regimes: the anisotropic expansion</p><p>for the high temperature regime and the radial breathing mode for</p><p>the low temperature regime. In order to consistently and</p><p>quantitatively extract the shear viscosity from these two</p><p>experiments, the hydrodynamic theory is utilized to derive the</p><p>universal hydrodynamic equations, which include both friction force</p><p>and heating arising from frictions. These equations are simplified</p><p>and solved, considering the universal properties of unitary Fermi</p><p>gases as well as the specific conditions for each experiment. Using</p><p>these universal hydrodynamic equations, shear viscosity is extracted</p><p>from the anisotropic expansion conducted at high temperatures and</p><p>the predicted $\eta\propto T^{3/2}$ scaling is demonstrated. The</p><p>demonstration of the high temperature scaling sets a benchmark for</p><p>measuring viscosity at low temperatures. For the low temperature</p><p>breathing mode experiment, the shear viscosity is directly related</p><p>to the damping rate of an oscillating cloud, through the same</p><p>universal hydrodynamic equations. The raw data from the previously</p><p>measured radial breathing experiments are carefully analyzed to</p><p>extract the shear viscosity. The low temperature data join with the</p><p>high temperature data smoothly, which presents the full measurement</p><p>of the quantum shear viscosity from nearly the ground state to the</p><p>two-body Boltzmann regime. The possible effects of the bulk</p><p>viscosity in the high temperature anisotropic expansion experiment</p><p>is also studied and found to be consistent with the predicted</p><p>vanishing bulk viscosity in the normal fluid phase at unitarity.</p><p>Using the measured shear viscosity $\eta$ and the previously</p><p>measured entropy density $s$, the ratio of $\eta/s$ is estimated and</p><p>therefore compared to a string theory limit, which conjectures</p><p>$\eta/s\geq\hbar/4\pi k_B$ for any fluid and defines a perfect fluid</p><p>when the equality is satisfied. It is found that $\eta/s$, for a</p><p>unitary Fermi gas at the normal-superfluid transition point, is</p><p>about $5$ times the string limit. This shows that our unitary Fermi</p><p>gas exhibit nearly perfect fluidity at low temperatures.</p><p>In addition to the quantum shear viscosity measurement, consistent</p><p>and accurate methods of calibrating the energy and temperature for</p><p>unitary Fermi gases is also developed in this thesis. While the</p><p>energy is calculated from the cloud dimensions by exploiting the</p><p>virial theorem, the temperature is determined using different</p><p>methods for different temperature regimes. At high temperatures, the</p><p>second virial coefficient approximation is applied to the energy</p><p>density, from which a variety of thermodynamic quantities, including</p><p>the temperature, are derived. For the low temperatures, the previous</p><p>calibration from the energy $E$ and entropy $S$ measurement is</p><p>improved by using a better calculation on the entropy and adding</p><p>more constraints at higher temperatures using the second virial</p><p>approximation. A power law curve with discontinues heat capacity is</p><p>then fitted to the $E$-$S$ curve and the temperature is obtained</p><p>using $\partial E/\partial S$. The energy and temperature</p><p>calibrations developed in this dissertation are universal and</p><p>therefore can be applied on other thermodynamic and hydrodynamic</p><p>experiments at unitarity.</p>