Eur. Phys. J. B 61, 277-285 (2008)
https://doi.org/10.1140/epjb/e2008-00084-2

Ground state properties of an asymmetric Hubbard model for unbalanced ultracold fermionic quantum gases

KOMET 337, Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 55099 Mainz, Germany

Corresponding author: ^a tobias.gottwald@uni-mainz.de

Received: 3 August 2007
Revised: 18 December 2007
Published online: 29 February 2008

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_↑≠t_↓) 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. We present the phase diagram of the homogeneous system and numerical results for unbalanced Fermi-mixtures obtained 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.