Superfluidity in a Degenerate Atomic Fermi Gas

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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.