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arXiv:1206.6740 · New Journal of Physics

Dynamics of cold bosons in optical lattices: effects of higher Bloch bands

Mateusz Łącki, Dominique Delande, Jakub Zakrzewski

Published Jan 29, 2013• 27 citations
arXivHTMLPDF

Abstract

The extended effective multiorbital Bose–Hubbard-type Hamiltonian which takes into account higher Bloch bands is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation to current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean-field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid–Mott insulator transition and the absorption spectroscopy, that is, the energy absorption rate when the lattice depth is periodically modulated.

DOI
10.1088/1367-2630/15/1/013062

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The extended effective multiorbital Bose–Hubbard-type Hamiltonian which takes into account higher Bloch bands is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation to current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean-field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid–Mott insulator transition and the absorption spectroscopy, that is, the energy absorption rate when the lattice depth is periodically modulated.
To describe a gas of cold bosonic atoms in the optical lattice, a discrete lattice hamiltonian, the BoseHubbard model is widely used. It simplifies description of phyics, by providing discretization, and its dependence on only two parameters: J — controling hopping of particles between different sites, and U describing on-site interacions. The model assumes restriction of physics to the lowest Bloch Band of the lattice and only local interaction. Recently a new appraoch [2] has been proposed. Instead of resctricting to the lowest Bloch band, a restriction to a smartly chosen subspace of the on-site hamiltonian takes place. The new, effective hamiltonian can be derived. It also has the form of the Bose-Hubbard hamiltonian, but with renormalized constants J and U; which become density-dependent. In our reseach we study what consequeces, the renormalization of hamiltonian parameters may have on a trapped bosonic atom gas experiments. We analyze phase diagrams of the homogeneous systems for different lattice geometries. We also focus on the renormalization procedure itself. We have found the renormalization procedure to be difficult and devious: we propose a new numerical approach that significantly enhances renormalization accuracy. In my talk I will briefly outline main results of our research.
The experimentally observed loss of superfluidity by introducing fermions to the boson Hubbard system on an optical lattice is explained. We show that the virtual transitions of bosons to higher Bloch bands, coupled with contact boson-fermion interactions of either sign, result in an effective increase of the boson on-site repulsion. If this renormalization of the on-site potential is dominant over the fermion screening of the boson interactions, the Mott insulating lobes of the Bose-Hubbard phase diagram will be enhanced for either sign of the boson-fermion interactions. We discuss the implications for cold-atom experiments where expansion of the Mott lobes by fermions has been conclusively established.
We study the phase diagram of a degenerate gas of bosons in an optical lattice, described by the boson Hubbard Hamiltonian, interacting with spin-polarized fermions. Virtual transitions of the bosons to the higher Bloch bands, coupled with the contact interspecies interactions of either sign, result in an effective increase of the bosonic on-site repulsion. If this renormalization of the on-site potential is dominant over the fermionic screening of the boson interactions, superfluid coherence of the Bose-Hubbard system will be reduced by the fermions. We discuss experimental implications for cold atomic systems.
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.
Abstract We perform the cluster mean-field with density matrix renormalization (CMFT+DMRG) calculation on the two-band extended Bose–Hubbard model to uncover the physics behind the discontinuous transitions observed in the one-dimensional shaken optical lattice with hybridized two lowest Bloch bands. We determine the superfluid, Mott insulator, and staggered superfluid phases associated with this model using the appropriate order parameters. We obtained the phase diagrams for two values of shaking amplitudes and illustrated the phases and nature of phase transitions. The transition from Mott insulator and superfluid to staggered superfluid is discontinuous for small shaking amplitudes. We analyse how the shaking frequency controls the effective chemical potential in the model and, consequently, the ground state energy that drives the discontinuous transition. Finally, we compare our results with those of earlier works.
By means of diffusion Monte Carlo calculations, we investigated the quantum phase transition between a superfluid and a Mott insulator for a system of hard-sphere bosons in a quasi-one-dimensional optical lattice. For this continuous Hamiltonian, we studied how the stability limits of the Mott phase changed with the optical lattice depth and the transverse confinement width. A comparison of these results to those of a one-dimensional homogeneous Bose-Hubbard model indicates that this last model describes accurately the phase diagram only in the limit of deep lattices. For shallow ones, our results are comparable to those of the sine-Gordon model in its limit of application. We provide an estimate of the critical parameters when none of those models are realistic descriptions of a quasi-one-dimensional optical lattice.