Population imbalanced fermions in harmonically trapped optical lattices

TL;DR

This paper investigates the ground state phases of population imbalanced fermions in two-dimensional optical lattices using the Bogoliubov-de Gennes formalism, revealing complex modulation patterns of the superfluid order parameter and unpaired fermion densities.

Contribution

It provides a detailed analysis of how the superfluid order parameter and unpaired fermion densities modulate in trapped optical lattices under various densities and imbalances, highlighting phase transition behaviors.

Findings

Order parameter modulates radially towards edges at low density

Single peak in unpaired fermion density at low and high imbalance

Double peaks in unpaired fermion density at intermediate imbalance

Abstract

The attractive Fermi-Hubbard Hamiltonian is solved via the Bogoliubov-de Gennes formalism to analyze the ground state phases of population imbalanced fermion mixtures in harmonically trapped two-dimensional optical lattices. In the low density limit the superfluid order parameter modulates in the radial direction towards the trap edges to accommodate the unpaired fermions that are pushed away from the trap center with a single peak in their density. However in the high density limit while the order parameter modulates in the radial direction towards the trap center for low imbalance, it also modulates towards the trap edges with increasing imbalance until the superfluid to normal phase transition occurs beyond a critical imbalance. This leads to a single peak in the density of unpaired fermions for low and high imbalance but leads to double peaks for intermediate imbalance.