Natural orbits of atomic Cooper pairs in a nonuniform Fermi gas

TL;DR

This paper investigates the natural pairing orbits of atomic Cooper pairs in an inhomogeneous Fermi gas, revealing their structure and entanglement properties within a spherical harmonic trap.

Contribution

It introduces a method to analyze Cooper pair wave functions using Schmidt decomposition and explores the spatial entanglement in a nonuniform Fermi gas.

Findings

Natural pairing orbits are identified in a trapped Fermi gas.

The wave function of Cooper pairs can be expressed via Schmidt decomposition.

Spatial entanglement between atoms in a pair is characterized.

Abstract

We examine the basic mode structure of atomic Cooper pairs in an inhomogeneous Fermi gas. Based on the properties of Bogoliubov quasi-particle vacuum, the single particle density matrix and the anomalous density matrix share the same set of eigenfunctions. These eigenfunctions correspond to natural pairing orbits associated with the BCS ground state. We investigate these orbits for a Fermi gas in a spherical harmonic trap, and construct the wave function of a Cooper pair in the form of Schmidt decomposition. The issue of spatial quantum entanglement between constituent atoms in a pair is addressed.