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

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.PACS. 03.75.Hh Static properties of condensates; thermodynamical, statistical, and structural properties -39.25.+k Atom manipulation (scanning probe microscopy, laser cooling, etc.) (see also 82.37.Gk STM and AFM manipulations of a single molecule in physical chemistry and chemical physics; for atom manipulation in nanofabrication and processing, see 81.16.Ta) -71.10.Fd Lattice fermion models (Hubbard model, etc.)

Ground-state properties of fermionic mixtures with mass imbalance in optical lattices

“…The last term is the energy of light and heavy atoms in the harmonic trapping potential. In accordance with similar studies for the asymmetric Hubbard model [9], we consider here the same trapping potential for both species of atoms.…”

“…The last term is the energy of light and heavy atoms in the harmonic trapping potential. In accordance with similar studies for the asymmetric Hubbard model (HM) [9], we consider here the same trapping potential for both species of atoms. Since in this spinless version of the FKM with a confining potential the f -heavy atom occupation number f † i f i of each site i commutes with the Hamiltonian (1), the f -heavy atom occupation number is a good quantum number, taking only two values: w i = 1 or 0, according to whether or not the site i is occupied by the heavy atom.…”

Effective Hamiltonian for a half-filled asymmetric ionic Hubbard chain with alternating on-site interaction

“…46 However, experiments with trapped ultracold atoms can actually engineer quantum many-body states and thus realize models of correlated fermions and bosons which are not available in usual solid-state structures. 47 Recent theoretical predictions of various unconventional superfluid or superconducting, [48][49][50][51][52][53][54] insulating 55,56 and magnetic 57 phases in such novel systems have further stimulated the interest in the spin-asymmetric Hubbard model.…”