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arXiv:cond-mat/0612170 · Physical Review A

Multiorbital mean-field approach for bosons, spinor bosons, and Bose-Bose and Bose-Fermi mixtures in real-space optical lattices

Ofir E. Alon, Alexej I. Streltsov, Lorenz S. Cederbaum

Published Jul 12, 2007• 13 citations
arXivHTMLPDF

Abstract

Cold atoms in optical lattices are described in real space by the multiorbital mean-field approach. We consider four typical systems: (i) spinless identical bosons, (ii) spinor identical bosons, (iii) Bose-Bose mixtures, and (iv) Bose-Fermi mixtures, and derive in each case the corresponding multiorbital mean-field energy functional and working equations. The general equations as well as those obtained by explicitly utilizing the translational symmetry of lattices are presented. We discuss the effects of particle-particle interactions and translational symmetry on properties of the solutions.

DOI
10.1103/physreva.76.013611

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Cold atoms in optical lattices are described in real space by the multiorbital mean-field approach. We consider four typical systems: (i) spinless identical bosons, (ii) spinor identical bosons, (iii) Bose-Bose mixtures, and (iv) Bose-Fermi mixtures, and derive in each case the corresponding multiorbital mean-field energy functional and working equations. The general equations as well as those obtained by explicitly utilizing the translational symmetry of lattices are presented. We discuss the effects of particle-particle interactions and translational symmetry on properties of the solutions.
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Quantum phases and phase transitions of weakly to strongly interacting bosonic atoms in deep to shallow optical lattices are described by a single multiorbital mean-field approach in real space. For weakly interacting bosons in one dimension, the critical value of the superfluid to Mott insulator (MI) transition found is in excellent agreement with many-body treatments of the Bose-Hubbard model. For strongly interacting bosons, (i) additional MI phases appear, for which two (or more) atoms residing in each site undergo a Tonks-Girardeau-like transition and localize, and (ii) on-site excitation becomes the excitation lowest in energy. Experimental implications are discussed.
We give a detailed discussion of the recently developed generalized dynamical mean-field theory (GDMFT) for a mixture of bosonic and fermionic particles. We show that this method is nonperturbative and exact in infinite dimensions, and reliably describes the full range from weak to strong coupling. Like in conventional dynamical mean-field theory, the small parameter is 1/z1/z1/z, where zzz is the lattice coordination number. We apply the GDMFT scheme to a mixture of spinless fermions and bosons in an optical lattice. We investigate the possibility of a supersolid phase, focusing on the case of 1/2 filling for the fermions and 3/2 filling for the bosons.
We study an atomic Bose-Fermi mixture with unpolarized fermions in an optical lattice. We obtain the Mott ground states of such a system in the limit of the deep optical lattice and discuss the effect of quantum fluctuations on these states. We also study the superfluid-insulator transitions of bosons and metal-insulator transition of fermions in such a mixture within a slave-rotor mean-field approximation, and obtain the corresponding phase diagram. We discuss experimental implications of our results.
We discuss the theory of mixtures of bosonic and fermionic atoms in periodic potentials at zero temperature. We derive a general Bose-Fermi Hubbard Hamiltonian in a one-dimensional optical lattice with a superimposed harmonic trapping potential. We study the conditions for linear stability of the mixture and derive a mean-field criterion for the onset of a bosonic superfluid transition. We investigate the ground-state properties of the mixture in the Gutzwiller formulation of mean-field theory, and present numerical studies of finite systems. The bosonic and fermionic density distributions and the onset of quantum phase transitions to demixing and to a bosonic Mott-insulator are studied as a function of the lattice potential strength. The existence is predicted of a disordered phase for mixtures loaded in very deep lattices. Such a disordered phase possessing many degenerate or quasidegenerate ground states is related to a breaking of the mirror symmetry in the lattice.
We consider a mixture of interacting bosons and fermions in optical lattices described by the Bose–Fermi Hubbard Hamiltonian. To treat bosonic degrees of freedom, we use a generalized dynamical mean field theory (GDMFT). By combining the GDMFT with the numerical renormalization group method, we revisit the zero-temperature phase diagram with particular emphasis on many-body effects in a supersolid state and discuss the origin of an anomalous peak structure emerging in the density of states for fermions.