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arXiv:1010.5553 · Physical Review Letters

Strongly Interacting Atom Lasers in Three-Dimensional Optical Lattices

Itay Hen, Marcos Rigol

Published Oct 26, 2010• 15 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.105.180401

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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 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.
Superfluid to Mott-insulator transitions in atomic Bose–Einstein condensates (BEC) in optical lattices are investigated for the case of number of atoms per site larger than one. To account for mean field repulsion between the atoms in each well, we construct an orthogonal set of Wannier functions. The resulting hopping amplitude and on-site interaction may be substantially different from those calculated with single-atom Wannier functions. As illustrations of the approach, we consider lattices of various dimensionality and different mean occupations. We find that in three-dimensional optical lattices the correction to the critical lattice depth is significant enough to be measured experimentally even for a small number of atoms. Finally, we discuss the validity of the single-band model.
Ultracold bosonic gases in optical lattices are strongly correlated quantum systems similar to solids. The strong correlation between the electrons in a solid on the one hand, and the bosonic atoms in optical lattice on the other, exhibit various quantum phenomena like insulation, conductivity, localization of electrons and atoms, respectively. Controlled by the intensity of the lattice laser, the ultracold bosonic gas can be transferred from a regime with superfluid character for shallow lattices into a regime of strong correlations, the Mott insulator. As an additional external parameter besides the lattice depth, one can generate spatial inhomogeneities by superimposing an additional standing wave (so-called two-color superlattices), which gives rise to localization effects or the formation of a Bose-glass phase. In the present work, numerical simulations are employed in order to investigate characteristic signatures of the quantum phases in the low-energy excitation spectrum of one-dimensional systems. We simulate temporal small amplitude modulations of the optical lattice in analogy to experiments, and evaluate the response of the system from the time-evolved initial state. The lattice systems are described in the framework of the Bose-Hubbard model. For the evaluation of the time-evolved state, we employ several numerical methods. We analyze systems of small size (6 particles on 6 sites) using an exact time-evolution by integration of the time-dependent Schrödinger equation. The formulation of an importance truncation scheme enables us to retain only the relevant components of the model space in the strongly correlated regime and, thus, allows for the investigation of systems with 10 particles on 10 sites using exact time-evolution. Based on this method, we present results of the Mott-insulating regime as well as for the Bose-glass phase. Furthermore, we employ particle-hole methods, which allow for the treatment of systems with experimental lattice sizes and particle numbers. Starting from the equation of motion method we adapt the Tamm-Dancoff approximation as well as the random-phase approximation for the occupation number representation of the Bose-Hubbard model. We present results of simulations of up to 50 particles on 50 sites and discuss the impact of the lattice depth on the low-energy excitations (U-resonance). Moreover, the impact of a two-color superlattice and the variation of its amplitude is investigated.
We study the spatiotemporal dynamics of interacting bosons on a two-dimensional Hubbard lattice in the strongly interacting regime, taking into account the dynamics of condensate amplitude as well as the direct transport of noncondensed fluctuations. To that end we develop a self-consistent density-matrix approach which goes beyond the standard Gutzwiller mean-field theory. Starting from the Liouville-von-Neumann equation we derive a quantum master equation for the time evolution of the system's local density matrix at each lattice site, with a dynamical bath that represents the rest of the system. We apply this method to the expansion dynamics of an initially prepared cloud of interacting bosons in an optical lattice. We observe a ballistic expansion of the condensate, as expected, followed by slow, diffusive transport of the normal bosons. We discuss, in particular, the robustness of the Mott insulator phase as well as its melting due to incoherent transport. The method should be applicable to various models of lattice bosons in the strongly correlated regime.
Abstract We explore the condensate phase of single-species bosons in an optical lattice through the use of dissipative Bose–Hubbard models. The ground state of system possesses a real-energy, which corresponds to non-Hermitian Hamiltonians with non-reciprocal hopping phase factors. Through the application of inhomogeneous dynamical Gutzwiller mean-field theory (DGMFT), we predict a fascinating phenomenon: the ground state displays a periodic arrangement of superfluid islands amidst a Mott insulator sea. Additionally, the number of superfluid islands is proportional to the spatial period squared.