Ground State Properties of an Asymmetric Hubbard Model for Unbalanced Ultracold Fermionic Quantum Gases

TL;DR

This paper investigates the ground state properties of an asymmetric Hubbard model for unbalanced ultracold fermionic gases, revealing complex shell structures and a novel magnetized superfluid phase through analytical and numerical methods.

Contribution

It introduces a detailed analysis of an asymmetric Hubbard model with spin-dependent hopping, highlighting new superfluid phases and shell structures in inhomogeneous ultracold gases.

Findings

Identification of shell structures with normal and superfluid phases

Discovery of a new magnetized superfluid phase

Analytical solutions for spin-independent hopping case

Abstract

In order to describe unbalanced ultracold fermionic quantum gases on optical lattices in a harmonic trap, we investigate an attractive ($U<0$) asymmetric ($t_\uparrow\neq t_\downarrow$) Hubbard model with a Zeeman-like magnetic field. In view of the model's spatial inhomogeneity, we focus in this paper on the solution at Hartree-Fock level. The Hartree-Fock Hamiltonian is diagonalized with particular emphasis on superfluid phases. For the special case of spin-independent hopping we analytically determine the number of solutions of the resulting self-consistency equations and the nature of the possible ground states at weak coupling. Numerical results for unbalanced Fermi-mixtures are presented within the local density approximation. In particular, we find a fascinating shell structure, involving normal and superfluid phases. For the general case of spin-dependent hopping we calculate the density of states and the possible superfluid phases in the ground state. In particular, we find a new magnetized superfluid phase.