BCS Theory for Trapped Ultracold Fermions

TL;DR

This paper extends BCS theory to trapped ultracold fermions, incorporating quantized energy levels and providing numerical results for critical temperature and gap, testing semi-classical approximations.

Contribution

It introduces a divergence-free BCS theory for trapped fermions using a pseudo-potential approach, including quantized energy levels.

Findings

Numerical critical temperature results for trapped fermions.

Temperature dependence of the energy gap.

Validation of semi-classical approximations.

Abstract

We develop an extension of the well-known BCS-theory to systems with trapped fermions. The theory fully includes the quantized energy levels in the trap. The key ingredient is to model the attractive interaction between two atoms by a pseudo-potential which leads to a well defined scattering problem and consequently a BCS-theory free of divergences. We present numerical results for the BCS critical temperature and the temperature dependence of the gap. They are used as a test of existing semi-classical approximations.