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arXiv:cond-mat/0407812 · Physical Review A

Fractional-filling loophole insulator domains for ultracold bosons in optical superlattices

Pierfrancesco Buonsante, Vittorio Penna, A. Vezzani

Published Dec 23, 2004• 54 citations
arXivHTMLPDF

Abstract

The zero-temperature phase diagram of a Bose-Einstein condensate confined in realistic one-dimensional $\mathit{\ensuremath{\ell}}$-periodic optical superlattices is investigated. The system of interacting bosons is modeled in terms of a Bose-Hubbard Hamiltonian whose site-dependent local potentials and hopping amplitudes reflect the periodicity of the lattice partition in $\mathit{\ensuremath{\ell}}$-site cells. Relying on the exact mapping between the hardcore limit of the boson Hamiltonian and the model of spinless noninteracting fermions, incompressible insulator domains are shown to exist for rational fillings that are predicted to be compressible in the atomic limit. The corresponding boundaries, qualitatively described in a multiple-site mean-field approach, are shown to exhibit an unusual loophole shape. A more quantitative description of the loophole domain boundaries at half filling for the special case $\mathit{\ensuremath{\ell}}=2$ is supplied in terms of analytic strong-coupling expansions and quantum Monte Carlo simulations.

DOI
10.1103/physreva.70.061603

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The zero-temperature phase diagram of a Bose-Einstein condensate confined in realistic one-dimensional \ensuremathℓ\mathit{\ensuremath{\ell}}\ensuremathℓ-periodic optical superlattices is investigated. The system of interacting bosons is modeled in terms of a Bose-Hubbard Hamiltonian whose site-dependent local potentials and hopping amplitudes reflect the periodicity of the lattice partition in \ensuremathℓ\mathit{\ensuremath{\ell}}\ensuremathℓ-site cells. Relying on the exact mapping between the hardcore limit of the boson Hamiltonian and the model of spinless noninteracting fermions, incompressible insulator domains are shown to exist for rational fillings that are predicted to be compressible in the atomic limit. The corresponding boundaries, qualitatively described in a multiple-site mean-field approach, are shown to exhibit an unusual loophole shape. A more quantitative description of the loophole domain boundaries at half filling for the special case \ensuremathℓ=2\mathit{\ensuremath{\ell}}=2\ensuremathℓ=2 is supplied in terms of analytic strong-coupling expansions and quantum Monte Carlo simulations.
Ultracold bosons in optical superlattices are expected to exhibit fractional-filling insulating phases for sufficiently large repulsive interactions. On strictly one-dimensional systems, the exact mapping between hard-core bosons and free spinless fermions shows that any periodic modulation in the lattice parameters causes the presence of fractional-filling insulator domains. Here, we focus on two recently proposed realistic two-dimensional structures where such mapping does not hold, i.e., the two-leg ladder and the trimerized kagom\'e lattice. Based on a cell strong-coupling perturbation technique, we provide quantitatively satisfactory phase diagrams for these structures, and give estimates for the occurrence of the fractional-filling insulator domains in terms of the intercell to intracell hopping amplitude ratio.
We report a multiple-site mean-field analysis of the zero-temperature phase diagram for ultracold bosons in realistic optical superlattices. The system of interacting bosons is described by a Bose-Hubbard model whose site-dependent parameters reflect the nontrivial periodicity of the optical superlattice. An analytic approach is formulated based on the analysis of the stability of a fixed-point of the map defined by the self-consistency condition inherent in the mean-field approximation. The experimentally relevant case of the period-2 one-dimensional superlattice is briefly discussed. In particular, it is shown that, for a special choice of the superlattice parameters, the half-filling insulator domain features an unusual loophole shape that the single-site mean-field approach fails to capture.
The phase diagram of ultracold bosons in realistic optical superlattices is addressed via second-order cell strong coupling perturbative expansions for the Bose-Hubbard model describing the system. Taking advantage of the cell partition inherent in the complex periodic modulation of a superlattice, this technique allows for the description of the unusual loophole-shaped insulator domains that may occur in the phase diagram of the system, unlike the standard perturbative approach. Furthermore, comparisons with quantum Monte Carlo simulations show that our approach provides quantitatively satisfactory results at a significantly lower computational cost than brute force numerical methods. We explicitly consider the phase diagrams for two realistic 3-periodic optical superlattices. These show that many insulator domains exhibit an unusual reentrant character, which we discuss, and suggest that the quantum phase transition relevant to the loophole-shaped insulating domains does not require extreme experimental condition in order to be observed.
We present an analytic description of the finite-temperature phase diagram of the Bose-Hubbard model, successfully describing the physics of cold bosonic atoms trapped in optical lattices and superlattices. Based on a standard statistical mechanics approach, we provide the exact expression for the boundary between the superfluid and the normal fluid by solving the self-consistency equations involved in the mean-field approximation to the Bose-Hubbard model. The zero-temperature limit of such a result supplies an analytic expression for the Mott lobes of superlattices, characterized by a critical fractional filling.
We use quantum Monte Carlo simulations and exact diagonalization to explore the phase diagram of the Bose-Hubbard model with an additional superlattice potential. We first analyze the properties of superfluid and insulating phases present in the hard-core limit where an exact analytic treatment is possible via the Jordan-Wigner transformation. The extension to finite on-site interactions is achieved by means of quantum Monte Carlo simulations. We determine insulator and superfluid phase diagrams as functions of the on-site repulsive interaction, superlattice potential strength, and filling, finding that insulators with fractional occupation numbers, which are present in the hard-core case, extend deep into the soft-core region. Furthermore, at integer fillings, we find that the competition between the on-site repulsion and the superlattice potential can produce a phase transition between a Mott insulator and a charge-density-wave insulator, with an intermediate superfluid phase. Our results are relevant to the behavior of ultracold atoms in optical superlattices which are beginning to be studied experimentally.
We study the topological properties of an extended Bose-Hubbard model with cyclically modulated hopping and on-site potential parameters, which can be realized with ultracold bosonic atoms in a one-dimensional optical superlattice. We show that the interacting bosonic chain at half filling and in the deep Mott insulating regime can simulate bosonic Chern insulators with a topological phase diagram similar to that of the Haldane model of noninteracting fermions. Furthermore, we explore the topological properties of the ground state by calculating the many-body Chern number, the quasiparticle energy spectrum with gapless edge modes, the topological pumping of the interacting bosons, and the topological phase transition from normal (trivial) to topological Mott insulators. We also present the global phase diagram of the many-body ground state, which contains a superfluid phase and two Mott insulating phases with trivial (a zero Chern number) and nontrivial topologies (a nonzero Chern number), respectively.