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arXiv:1312.6269 · Canadian Journal of Physics

Normal and anomalous densities in Bose–Einstein condensates with optical lattices

M. Bendacha, Abdelâali Boudjemâa

Published Nov 12, 2013• 2 citations
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Abstract

We study the quantum phase transition from the superfluid to the Mott insulator state in two- and three-dimensional Bose–Einstein condensate with optical lattices using Bose–Hubbard Hamiltonian within the generalized Hatree–Fock–Bogoliubov approximation. The behavior of the depletion and the anomalous fraction has been investigated in the Mott insulator phase. We found that at T = 0, these quantities become significant in two and three dimensions. It is shown also that the dimensionality of the lattice enhances the anomalous density.

DOI
10.1139/cjp-2013-0396

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We study the quantum phase transition from a superfluid to a Mott insulator in optical lattices using a Bose-Hubbard Hamiltonian. For this purpose we develop a field theoretical approach in terms of path integral formalism to calculate the second-order quantum corrections to the energy density as well as to the superfluid fraction in cubic optical lattices. Using the present approach, the condensate fraction and ground-state energy are calculated as functions of the sss-wave scattering length. In contrast to the Bogoliubov model, which is, technically speaking, a one-loop approximation, we carry the calculation up to two loops and improve the result further by variational perturbation theory. The result suggests that the quantum phase transition exists.
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We use the Bogoliubov theory of atoms in an optical lattice to study the approach to the Mott-insulator transition. We derive an explicit expression for the superfluid density based on the rigidity of the system under phase variations. This enables us to explore the connection between the quantum depletion of the condensate and the quasi-momentum distribution on the one hand and the superfluid fraction on the other. The approach to the insulator phase may be characterized through the filling of the band by quantum depletion, which should be directly observable via the matter–wave interference patterns. We complement these findings by self-consistent Hartree–Fock–Bogoliubov–Popov calculations for one-dimensional lattices, including the effects of a parabolic trapping potential.
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