One-dimensional harmonically confined SU(N) fermions

Abstract

We study the momentum distributions and spatial correlations of few harmonically confined SU($N$) fermions using quantum Monte Carlo methods. In our study, we vary the spin degeneracy $N$ from 2 to 6 and the total number of particles from 6 to 18. Only balanced mixtures, with the same number of atoms per spin type, and repulsive unlike-spin contact interactions are considered. Going from $N=2$ to $N=6$, with the same occupancy of each spin state, we observe an increase of atom-atom correlations. This effect is particularly significant in the momentum distributions, which show fatter tails at large $k$ ($k\ensuremath{\sigma}\phantom{\rule{0.16em}{0ex}}>\phantom{\rule{0.16em}{0ex}}5, \ensuremath{\sigma}$ being the oscillator length) when $N$ grows, in agreement with experimental findings. Those tails also show the expected ${k}^{\ensuremath{-}4}$ decay related to the Tan contact for different values of the spin degeneracy. According to our results, the local spin ordering and the spin-spin correlations are mainly determined by $N$ via the Pauli exclusion principle, with minor influences from the particle-particle interactions, irrespective of the total number of confined atoms.