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Journal of Physics A Mathematical and Theoretical

Superfluid-to-Mott transition in optical lattices with restricted geometry

T. A. Zaleski, T. K. Kopeć

Published Oct 4, 2010• 12 citations
Publisher

Abstract

We study the influence of the restricted geometry of a cubic lattice confined within a finite slab of L layers (i.e. of the form ∞ × ∞ × L ) on the ground-state properties of interacting bosons in the optical lattice. Using the quantum rotor approach for the Bose–Hubbard model, we quantify how the restricted slab geometry affects the superfluid-to-Mott-insulator transition. For increasing values of L , both the analytical approach for large L and the direct calculation using lattice density of states for any arbitrary L show that the behavior of the system becomes indistinguishable from the cubic bulk case ( L = ∞ ) even for relatively small values of L ( L ≈ 10). This may be an important justification for treating bosons in optical lattices using methods of statistical physics pertinent for infinite systems.

DOI
10.1088/1751-8113/43/42/425303

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We present a study of the superfluid properties of atomic Bose gases in optical lattice potentials using the Bose-Hubbard model. To do this, we use a microscopic definition of the superfluid fraction based on the response of the system to a phase variation imposed by means of twisted boundary conditions. We compare the superfluid fraction to other physical quantities, i.e., the interference pattern after ballistic expansion, the quasimomentum distribution, and number fluctuations. We have performed exact numerical calculations of all these quantities for small one-dimensional systems. We show that the superfluid fraction alone exhibits a clear signature of the Mott-insulator transition. Observables like the fringe visibility, which probe only ground-state properties, do not provide direct information on superfluidity and the Mott-insulator transition.
Abstract The physics of the Bose–Hubbard (BH) model is the subject of intensive studies in recent years, since it has been realized that BH Hamiltonian can be applied to systems of cold atoms confined in periodic optical lattice potential, where the effects on interactions are strongly enhanced. Our aim is to extend the widely used mean‐field treatment of the superfluid–Mott insulator (SF–MI) transition in the BH model. Our method also improves the strong‐coupling expansion that works well only for sufficiently large insulating gap. The key point of the approach is to consider the representation of strongly interacting bosons as particles with attached U(1) gauge group flux tubes, which constitutes the quantum rotor description. The effective action formalism allows us to cast the problem in terms of the phaseonly action and obtain an analytical formulas for critical lines. Finally, we calculate the zero‐temperature SF–MI phase diagrams for three‐dimensional BH model and compare our results with the outcome of numerical Monte Carlo simulations. We found a very good agreement for the quantitative results regarding the details of the lobe in the phase diagrams showing the quantum transition from superfluid to the Mott insulating phase (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We investigate the excitations of strongly interacting bosons confined in an optical lattice. Using the combined Bogoliubov method and the quantum rotor approach, we map the Hamiltonian of strongly interacting bosons onto U(1) phase action. This allows us to calculate the density of states for various geometries of optical lattices and its dependence on the presence of the superfluid phase. We observe that the superfluidity is manifested by a sharp coherence peak resulting from long-range order, while the excitation spectrum of the Mott insulator contains a gap.