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arXiv:1201.3788 · Physical Review A

Atom-atom correlations in time-of-flight imaging of ultracold bosons in optical lattices

T. A. Zaleski, T. K. Kopeć

Published Nov 14, 2011• 28 citations
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Abstract

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.

DOI
10.1103/physreva.84.053613

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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.
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.
The density-density correlations of ultracold Bosons released from a two-dimensional square optical lattice are investigated based on the quantum phase field U (1) rotor field. With the effects of the particle number fluctuations and the phase degrees of freedom taken into consideration, the theory can be used to describe the cold atom system with strong interaction. Using this theory, the characteristics of ultracold atom gas in the process in which the superfluid state of optical lattice transits to insulating state, are well described. The results show that in the patterns of the density-density correlations, the continuous diagonal lines gradually transit to scattered peaks. The results match the experimental ones. In addition, the effects of the quantum depletion on the density-density correlation are also included in the result, and the relevant conclusions are also consistent with the existing theoretical and experimental results.