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

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  • T. Gottwald
  • P. G.J. van Dongen

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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Suggested Citation

  • T. Gottwald & P. G.J. van Dongen, 2008. "Ground state properties of an asymmetric Hubbard model for unbalanced ultracold fermionic quantum gases," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(3), pages 277-285, February.
    • Handle: RePEc:spr:eurphb:v:61:y:2008:i:3:p:277-285
    DOI: 10.1140/epjb/e2008-00084-2
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