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arXiv:1108.1192 · Physical Review A

Expansion of Bose-Hubbard Mott insulators in optical lattices

Mark Jreissaty, Juan Carrasquilla, F. Alexander Wolf, Marcos Rigol

Published Oct 10, 2011• 32 citations
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Abstract

We study the expansion of bosonic Mott insulators in the presence of an optical lattice after switching off a confining potential. We use the Gutzwiller mean-field approximation and consider two different setups. In the first one, the expansion is restricted to one direction. We show that this leads to the emergence of two condensates with well-defined momenta, and argue that such a construct can be used to create atom lasers in optical lattices. In the second setup, we study Mott insulators that are allowed to expand in all directions in the lattice. In this case, a simple condensate is seen to develop within the mean-field approximation. However, its constituent bosons are found to populate many nonzero momentum modes. An analytic understanding of both phenomena in terms of the exact dispersion relation in the hard-core limit is presented.

DOI
10.1103/physreva.84.043610

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We study the expansion of bosonic Mott insulators in the presence of an optical lattice after switching off a confining potential. We use the Gutzwiller mean-field approximation and consider two different setups. In the first one, the expansion is restricted to one direction. We show that this leads to the emergence of two condensates with well-defined momenta, and argue that such a construct can be used to create atom lasers in optical lattices. In the second setup, we study Mott insulators that are allowed to expand in all directions in the lattice. In this case, a simple condensate is seen to develop within the mean-field approximation. However, its constituent bosons are found to populate many nonzero momentum modes. An analytic understanding of both phenomena in terms of the exact dispersion relation in the hard-core limit is presented.
We show that the dynamical melting of a Mott insulator in a three-dimensional lattice leads to condensation at nonzero momenta, a phenomenon that can be used to generate strongly interacting atom lasers in optical lattices. For infinite on-site repulsion, the case considered here, the momenta at which bosons condense are determined analytically and found to have a simple dependence on the hopping amplitudes. The occupation of the condensates is shown to scale linearly with the total number of atoms in the initial Mott insulator. Our results are obtained by using a Gutzwiller-type mean-field approach, gauged against exact-diagonalization solutions of small systems.
We review recent exact results for the free expansion of impenetrable bosons on one-dimensional lattices, after switching off a confining potential. When the system is initially in a superfluid state, far from the regime in which the Mott-insulator appears in the middle of the trap, the momentum distribution of the expanding bosons rapidly approaches the momentum distribution of non-interacting fermions. Remarkably, no loss in coherence is observed in the system as reflected by a large occupation of the lowest eigenstate of the one-particle density matrix. In the opposite limit, when the initial system is a pure Mott insulator with one particle per lattice site, the expansion leads to the emergence of quasicondensates at finite momentum. In this case, one-particle correlations like the ones shown to be universal in the equilibrium case develop in the system. We show that the out-of-equilibrium behavior of the Shannon information entropy in momentum space, and its contrast with one of non-interacting fermions, allows to differentiate the two different regimes of interest. It also helps in understanding the crossover between them.
The Bose-Hubbard model of a twofold degenerate Bose gas is studied in an optical lattice with one particle per site and virtual tunneling to empty and doubly occupied sites. An effective Hamiltonian for this system is derived within a continued-fraction approach. The ground state of the effective model is studied in mean-field approximation for a modulated optical lattice. A dimerized mean-field state gives a Mott insulator whereas the lattice without modulations develops long-range correlated phase fluctuations due to a Goldstone mode. This result is discussed in comparison with the superfluid and the Mott-insulating state of a single-component hard-core Bose gas.
We study the Mott-insulator transition of bosonic atoms in optical lattices. Using perturbation theory, we analyze the deviations from the mean-field Gutzwiller ansatz, which become appreciable for intermediate values of the ratio between hopping amplitude and interaction energy. We discuss corrections to number fluctuations, order parameter, and compressibility. In particular, we improve the description of the short-range correlations in the one-particle density matrix. These corrections are important for experimentally observed expansion patterns, both for bulk lattices and in a confining trap potential.
We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory.