Pairing of a harmonically trapped fermionic Tonks-Girardeau gas

TL;DR

This paper studies the pairing properties of a one-dimensional fermionic Tonks-Girardeau gas under harmonic confinement, revealing partial off-diagonal long-range order through analytical and numerical methods.

Contribution

It provides the first analysis of off-diagonal long-range order in a harmonically trapped FTG gas, deriving a closed-form two-particle density matrix and identifying partial pairing.

Findings

Largest eigenvalue of two-body density matrix scales as N/2

Partial off-diagonal long-range order is present in the trapped FTG gas

Analytical and numerical methods confirm pairing tendencies

Abstract

The fermionic Tonks-Girardeau (FTG) gas is a one-dimensional spin-polarized Fermi gas with infinitely strong attractive zero-range odd-wave interactions, arising from a confinement-induced resonance reachable via a three-dimensional p-wave Feshbach resonance. We investigate the off-diagonal long-range order (ODLRO) of the FTG gas subjected to a longitudinal harmonic confinement by analyzing the two-particle reduced density matrix for which we derive a closed-form expression. Using a variational approach and numerical diagonalization we find that the largest eigenvalue of the two-body density matrix is of order N/2, where N is the total particle number, and hence a partial ODLRO is present for a FTG gas in the trap.