# Universal quantum viscosity in a unitary Fermi gas.

Date

2012
Author

Advisors

Thomas, John E

Bass, Steffen

Behringer, Robert

Howell, Calvin

Wu, Ying

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Abstract

Unitary Fermi gases, first observed by our group 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 component6Li unitary Fermi gas is created through a collisional Feshbach
resonance centered near 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 crosses several fields.This dissertation reports the
first measurement of the quantum shear viscosity in a6Li unitary Fermi gas, which
is also the first measurement of a transport coefficient for a unitary Fermi gas.
While equilibrium thermodynamic quantities have been theoretically and experimentally
studied for the past few year, the measurement of a transport coefficient for a unitary
Fermi gas provides new challenges for state of the art nonperturbative many-body theory
as transport coefficients are more difficult to calculate than equilibrium thermodynamic
quantities. Two hydrodynamic experiments are employed to measure the shear viscosityηin
different temperature regimes: an isotropic expansion is used for the high temperature
regime and radial breathing mode is employed for the low temperature regime. In order
to consistently and quantitatively extract the shear viscosity from these two experiments,
hydrodynamic theory is utilized to derive universal hydrodynamic equations, which
include both the friction force and the heating arising from viscosity. These equations
are simplified and solved by 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 an isotropic expansion
conducted at high temperatures and the predicted η ∝ T3/2 universal 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, using 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 yields 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
an isotropic 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 viscosityηand the previously measured entropy densitys, the ratio
of η/s is estimated and compared to a string theory conjecture, which suggests that
η/s≥~/4πkB for a broad class of strongly interacting quantum fluids and defines a
perfect fluid when the equality is satisfied. It is found that η/s is about 5 times
the string theory limit, for a unitary Fermi gas at the normal-superfluid transition
point. This shows that our unitary Fermi gas exhibit nearly perfect fluidity at low
temperatures. As presented part of this dissertation is the development of consistent
and accurate methods of calibrating the energy and temperature for unitary Fermi gases.
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, a universal second virial coefficient approximation
is applied to the energy density, from which a variety of thermodynamic quantities,
including the temperature, are derived in terms of the measured cloud size. For low
temperatures, the previous calibration from the energy E and entropy S measurement
is improved by using a better calculation of the entropy and adding constraints at
high temperatures, using the second virial approximation. A power law curve with a
discontinuous heat capacity is then fitted to the E-Scurve and the temperature is
obtained using ∂ E/∂S. The energy and temperature calibrations developed in this dissertation
are universal and therefore can be applied to other thermodynamic and hydrodynamic
experiments at unitarity.

Type

DissertationDepartment

PhysicsPermalink

https://hdl.handle.net/10161/5453Citation

Cao, Chenglin (2012). *Universal quantum viscosity in a unitary Fermi gas.*Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/5453.

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