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Journal of Physics B Atomic Molecular and Optical Physics

Optical weight transfer in excitation spectra of ultra-cold bosons in two- and three-dimensional optical lattices

T. A. Zaleski

Published Jul 4, 2012• 7 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/45/14/145303

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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.
The excitations of strongly interacting bosons confined in a two-dimensional square lattice are studied. Using a combined Bogoliubov method and the quantum-rotor approach, the Hamiltonian of strongly interacting bosons is mapped onto the U(1)U(1)U(1)-phase action. This allows to calculate the momentum- and energy-resolved one-particle spectral function and its dependence on the presence of the superfluid phase. It is shown that the destruction of the ordered phase leads to the opening of the gap in the excitation spectrum in k=0\mathbf{k}=\mathbf{0}k=0. On the other hand, superfluidity manifests itself as a sharp coherence peak resulting from the emergence of the long-range order. Correlation effects lead to the appearance of a smearing of the band structure of incoherent particles although the remnants of the Bogoliubov excitations are still present in the coherent part of the spectrum.
We study the critical behavior near the quantum critical point of strongly interacting bosons placed 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)U(1)U(1) phase action in order to calculate analytically the density profiles as a function of hopping and reduced chemical potential. Our approach allows us to explicitly compute the scaling form of the density ns{n}_{s}ns​ for systems confined in two-dimensional square and three-dimensional cubic lattices. We find a good convergence of ns{n}_{s}ns​ with the universal scaling function in a wide temperature range that is accessible in the current experiments on the density profiles in cold bosonic systems.
Ultracold atoms in optical lattices have been intensively investigated in recent years as they provide a very well controllable environment for observation of many-body quantum phenomena, closely mimicking physics of strongly interacting electronic systems.Here, we use the quantum rotor approach supplemented by the Bogolyubov method to investigate one-and two-particle excitations, which are a measure of inter-particle correlations.We calculate one-particle spectral function and dynamic structure factor, which can be observed using spectroscopy of cold atomic systems.Our calculations require a significant numerical effort to determine multidimensional convolutions of momentum and frequency dependent constituents functions, which we achieve using parallelised fast Fourier transform.We observe the appearance of sharp coherence peaks in the superfluid phase of the cold bosons, which closely resembles the formation of sharply defined quasiparticle excitations below Tc in cuprates or smeared excitation spectra characteristic for strongly interacting systems.
We study ultra-cold bosonic systems in optical lattice using quantum rotor approach to calculate the currentcurrent correlations, which provides the information about conductivity of the system.The method allows us to go beyond mean-field approximation and track the behavior of the real part of the conductivity along the phase transition between the Mott insulator and superfluid state for various geometries of the lattice.In the phaseordered state at zero temperature, a discrete ingredient appears resulting from the long-range coherence in the system.
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 study the spatial correlations of strongly interacting bosons in a ground state, confined in a two-dimensional square and a three-dimensional cubic lattice. Using the combined Bogoliubov method and the quantum rotor approach, we map the Hamiltonian of strongly interacting bosons onto U(1) phase action in order to calculate the atom-atom correlations' decay along the principal axis and a diagonal of the lattice-plane direction as a function of distance. Lower tunneling rates lead to quicker decays of the correlations, whose character becomes exponential. Finally, correlation functions allow us to calculate quantities that are directly bound to experimental outcomes, namely time-of-flight absorption images and resulting visibility. Our results contain all the characteristic features present in experimental data (transition from Mott insulating blob to superfluid peaks, etc.), emphasizing the usability of the proposed approach.