## Superfluidity in a Degenerate Atomic Fermi Gas

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##### Date

2003-11-25##### Author

Nygaard, Nicolai

##### Advisor

Alexander, Millard H

Clark, Charles W

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Show full item record##### Abstract

Dilute atomic gases have become a powerful tool for studying
many-body quantum mechanics. The best example of this is the
achievement of Bose-Einstein condensation in 1995 in a gas of Bose atoms, a discovery which has invoked a confluence of ideas from condensed matter, atomic and nuclear physics. Now a concerted research effort is focused on creating and studying a BCS superfluid in an atomic Fermi gas.
In the work presented here we study in detail pairing
superfluidity in a Fermi gas of atoms, by self-consistently solving
the Bogoliubov-de Gennes equations, both for bulk systems, and for atoms in a harmonic confining potential. A critical part of this
work is the derivation of a regularized theory, which is formulated
entirely in terms of physically measurable quantities, such that a
quantitative comparison between theory and experiment is possible with no adjustable parameters. The resulting equations form a non-linear problem, and the accurate numerical solution of this poses a formidable challenge. A major component of this thesis is the development of efficient computational approaches to overcome these difficulties.
Based on the linear response of the gas to a twisting of the order
parameter phase, the superfluid density can be defined as a
generalized elasticity of the system. Using finite temperature
perturbation theory we calculate the superfluid density in an inhomogeneous system.
We investigate the structure and thermodynamic properties of a
singly quantized vortex line in a gas of superfluid fermionic
atoms, making the first quantitative determination the
critical rotation frequency for thermodynamic stability of the
vortex state, and study the nature of the bound states in the vortex core. These excitations fill the core, making direct imaging of the vortex unlikely. Instead, we propose an experiment to indirectly probe the vortex density of states with laser fields, in a scheme analogous to Scanning Tunneling Microscopy.
Furthermore, it is shown that the vortex state causes a shift of the
superfluid transition temperature, which can be understood as a finite size effect.

University of Maryland, College Park, MD 20742-7011 (301)314-1328.

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