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# Universal Quantum Viscosity in a Unitary Fermi Gas

## DukeSpace

 dc.contributor.advisor Thomas, John E en_US dc.contributor.author Cao, Chenglin en_US dc.date.accessioned 2012-05-25T20:10:57Z dc.date.available 2012-05-25T20:10:57Z dc.date.issued 2012 en_US dc.identifier.uri http://hdl.handle.net/10161/5453 dc.description Dissertation en_US dc.description.abstract

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 $^6$Li unitary Fermi gas is created through a colliosnal

Feshbach resonance centered around $834$G, 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 $^6$Li 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 $\eta\propto T^{3/2}$ 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

$\eta/s\geq\hbar/4\pi k_B$ 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 $\partial E/\partial S$. The energy and temperature

calibrations developed in this dissertation are universal and

therefore can be applied on other thermodynamic and hydrodynamic

experiments at unitarity.

en_US dc.subject Physics en_US dc.subject Optics en_US dc.subject Atomic physics en_US dc.subject Perfect Fluid en_US dc.subject Quantum Viscsoity en_US dc.subject Unitary Fermi Gas en_US dc.title Universal Quantum Viscosity in a Unitary Fermi Gas en_US dc.type Dissertation en_US dc.department Physics en_US