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AIP conference proceedings

Mott domains of bosons and fermions confined in optical lattices

Marcos Rigol

Published Jan 1, 2003• 0 citations
Publisher

Abstract

We study the ground state properties of the 1‐D boson and fermion Hubbard models in harmonic traps with an underlying lattice. The physics of these systems is found to be fundamentally different from the homogeneous case. Global quantities lose their meaning and Mott domains appear for a continuous range of incommensurate fillings. A local order parameter is defined to characterize the Mott insulating phases that coexist with the metallic ones. Finally, the phase diagrams show richer structures than in the homogeneous models.

DOI
10.1063/1.1612396

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We study the ground state properties of the 1‐D boson and fermion Hubbard models in harmonic traps with an underlying lattice. The physics of these systems is found to be fundamentally different from the homogeneous case. Global quantities lose their meaning and Mott domains appear for a continuous range of incommensurate fillings. A local order parameter is defined to characterize the Mott insulating phases that coexist with the metallic ones. Finally, the phase diagrams show richer structures than in the homogeneous models.
Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent, Mott-insulating domains always coexist with metallic regions, such that global quantities are not appropriate to describe the system. We define a local compressibility that characterizes the Mott-insulating regions and analyze other local quantities. It is shown that the momentum distribution function, a quantity that is commonly considered in experiments, fails in giving a clear signal of the Mott-insulating transition. Furthermore, we analyze a mean-field approach to these systems and compare it with the numerically exact QMC results. Finally, we determine a generic form for the phase diagram that allows us to predict the phases to be observed in the experiments.
In the absence of a confining potential, the boson-Hubbard model exhibits a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong coupling. We use quantum Monte Carlo simulations to study the ground state of the one-dimensional bosonic Hubbard model in a trap. Some, but not all, aspects of the Mott insulating phase persist. Mott behavior occurs for a continuous range of incommensurate fillings, very different from the unconfined case, and the establishment of the Mott phase does not proceed via a traditional quantum phase transition. These results have important implications for interpreting experiments on ultracold atoms on optical lattices.
Using quantum Monte Carlo (QMC) simulations we study the ground state properties of the one‐dimensional fermionic Hubbard model in traps with an underlying lattice. We show that this model displays quantum critical behavior at the boundaries of the local Mott‐insulating regions. A local compressibility defined to characterize the Mott‐insulating phase has a non‐trivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We study the momentum distribution function and we find that it is not appropriate to characterize the transitions in the system.
We use quantum Monte Carlo simulations to obtain zero-temperature state diagrams for strongly correlated lattice bosons in one and two dimensions under the influence of a harmonic confining potential. Since harmonic traps generate a coexistence of superfluid and Mott insulating domains, we use local quantities such as the quantum fluctuations of the and a local compressibility to identify the phases present in the inhomogeneous profiles. We emphasize the use of the characteristic density to produce a state diagram that is relevant to experimental optical lattice systems, regardless of the number of bosons or trap curvature and of the validity of the local-density approximation. We show that the critical value of U/t at which Mott insulating domains appear in the trap depends on the filling in the system, and it is in general greater than the value in the homogeneous system. Recent experimental results by Spielman et al. [Phys. Rev. Lett. 100, 120402 (2008)] are analyzed in the context of our two-dimensional state diagram, and shown to exhibit a value for the critical point in good agreement with simulations. We also study the effects of finite, but low (T<t/2), temperatures. We find that in two dimensions they have little influence on our zero-temperature results, while their effect is more pronounced in one dimension.
We use quantum Monte Carlo simulations to obtain zero-temperature state diagrams for strongly correlated lattice bosons in one and two dimensions under the influence of a harmonic confining potential. Since harmonic traps generate a coexistence of superfluid and Mott insulating domains, we use local quantities such as the quantum fluctuations of the density and a local compressibility to identify the phases present in the inhomogeneous density profiles. We emphasize the use of the ``characteristic density'' to produce a state diagram that is relevant to experimental optical lattice systems, regardless of the number of bosons or trap curvature and of the validity of the local-density approximation. We show that the critical value of U/tU/tU/t at which Mott insulating domains appear in the trap depends on the filling in the system, and it is in general greater than the value in the homogeneous system. Recent experimental results by Spielman et al. [Phys. Rev. Lett. 100, 120402 (2008)] are analyzed in the context of our two-dimensional state diagram, and shown to exhibit a value for the critical point in good agreement with simulations. We also study the effects of finite, but low $(T\ensuremath{\le}t/2)$, temperatures. We find that in two dimensions they have little influence on our zero-temperature results, while their effect is more pronounced in one dimension.
We studied the appearance of Mott insulator domains of hard sphere bosons on quasi-one-dimensional optical lattices when a harmonic trap was superimposed along the main axis of the system. Instead of the standard approximation represented by the Bose-Hubbard model, we described those arrangements by continuous Hamiltonians that depended on the same parameters as the experimental setups. We found that for a given trap the optical potential depth, V0{V}_{0}V0​, needed to create a single connected Mott domain decreased with the number of atoms loaded on the lattice. If the confinement was large enough, it reached a minimum when, in the absence of any optical lattice, the atom density at the center of the trap was the equivalent of one particle per optical well. For larger densities, the creation of that single domain proceeded via an intermediate shell structure in which Mott domains alternated with superfluid ones.