Phase separation of trapped spin-imbalanced Fermi gases in one-dimensional optical lattices

TL;DR

This paper investigates the phase separation phenomena in trapped spin-imbalanced Fermi gases within one-dimensional optical lattices, revealing how interactions influence polarization and pairing behavior through theoretical and numerical methods.

Contribution

It combines Bethe ansatz, local density approximation, and DMRG to analyze phase separation and critical polarization in 1D optical lattice Fermi gases, highlighting differences from continuum systems.

Findings

Shell structure with polarized core and paired wings predicted by LDA.

DMRG confirms phase separation at large particle numbers.

Critical polarization varies non-monotonically with interaction strength.

Abstract

We calculate the density profiles of a trapped spin-imbalanced Fermi gas with attractive interactions in a one-dimensional optical lattice, using both the local density approximation (LDA) and density matrix renormalization group (DMRG) simulations. Based on the exact equation of state obtained by Bethe ansatz, LDA predicts that the gas phase-separates into shells with a partially polarized core and fully paired wings, where the latter occurs below a critical spin polarization. This behavior is also seen in numerically exact DMRG calculations at sufficiently large particle numbers. Unlike the continuum case, we show that the critical polarization is a non monotonic function of the interaction strength and vanishes in the limit of large interactions.