# Trapped imbalanced fermionic superfluids in one dimension: A variational approach

## TL;DR

This paper introduces a variational wave function for a one-dimensional, population-imbalanced Fermi gas that captures FFLO pairing correlations and matches experimental density profiles, revealing oscillations in correlations rather than densities.

## Contribution

It develops a variational approach that models FFLO states in trapped imbalanced fermionic gases, linking order parameter oscillations to observable correlations.

## Key findings

- Large spatial oscillations of the order parameter in the strongly interacting regime.
- Density profiles align with experimental and Bethe ansatz results.
- Order parameter oscillations are detectable in density-density correlations, not densities.

## Abstract

We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approximation. Although we find no signature of the FFLO state in the densities of the two fermion species, we show that the oscillations of the order parameter appear in density-density correlations, both in-situ and after free expansion. Furthermore, above a critical polarization, the value of which depends on the interaction, we find the unpaired Fermi-gas state to be energetically more favorable.