Exact one-particle density matrix for SU($N$) fermionic matter-waves in the strong repulsive limit

TL;DR

This paper derives an exact expression for the one-particle density matrix of strongly repulsive SU(N) fermions in a ring trap, revealing how interactions, magnetic fields, and component number influence their momentum distribution.

Contribution

It introduces a Bethe ansatz approach to compute the correlation matrix for SU(N) fermions in the strong repulsive limit, applicable to mesoscopic systems beyond numerical reach.

Findings

Exact momentum distribution dependence on interaction, magnetic field, and N.

Correlation matrix computed for finite particle numbers and system sizes.

Analysis relevant for cold atom interference experiments.

Abstract

We consider a gas of repulsive $N$-component fermions confined in a ring-shaped potential, subject to an effective magnetic field. For large repulsion strengths, we work out a Bethe ansatz scheme to compute the two-point correlation matrix and then the one-particle density matrix. Our results holds in the mesoscopic regime of finite but sufficiently large number of particles and system size that are not accessible by numerics. We access the momentum distribution of the system and analyse its specific dependence of interaction, magnetic field and number of components $N$. In the context of cold atoms, the exact computation of the correlation matrix to determine the interference patterns that are produced by releasing cold atoms from ring traps is carried out.