Effects of the trapping potential on a superfluid atomic Fermi Gas

TL;DR

This paper investigates how a harmonic trapping potential affects the properties of a superfluid atomic Fermi gas, providing analytical and numerical insights into critical temperature, superfluid gap, and collective modes relevant for experiments.

Contribution

It presents an effective Hamiltonian approach to analytically determine key superfluid properties in a trapped Fermi gas, aligning with numerical results and aiding experimental observation.

Findings

Trapping potential significantly influences superfluid properties.

Analytical expressions for critical temperature and collective modes are derived.

Results support experimental detection of superfluid transition in trapped gases.

Abstract

We examine a dilute two-component atomic Fermi gas trapped in a harmonic potential in the superfluid phase. For experimentally realistic parameters, the trapping potential is shown to have crucial influence on various properties of the gas. Using an effective hamiltonian, analytical results for the critical temperature, the temperature dependence of the superfluid gap, and the energy of the lowest collective modes are derived. These results are shown to agree well with numerical calculations. We furthermore discuss in more detail a previous proposed method to experimentally observe the superfluid transition by looking at the collective mode spectrum. Our results are aimed at the present experimental effort to observe a superfluid phase transition in a trapped atomic Fermi gas.