Superfluid and Mott Insulating shells of bosons in harmonically confined optical lattices

Abstract

Weakly interacting atomic or molecular bosons in quantum degenerate regime and trapped in harmonically confined optical lattices, exhibit a wedding cake structure consisting of insulating (Mott) shells. It is shown that superfluid regions emerge between Mott shells as a result of fluctuations due to finite hopping. It is found that the order parameter equation in the superfluid regions is not of the Gross-Pitaeviskii type except near the insulator to superfluid boundaries. The excitation spectra in the Mott and superfluid regions are obtained, and it is shown that the superfluid shells posses low energy sound modes with spatially dependent sound velocity described by a local index of refraction directly related to the local superfluid density. Lastly, the Berezinskii-Kosterlitz-Thouless transition and vortex-antivortex pairs are discussed in thin (wide) superfluid shells (rings) limited by three (two) dimensional Mott regions.

11 pages, 9 figures,

References in corpus (10)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Cold bosonic atoms in optical lattices
• Transition from a strongly interacting 1D superfluid to a Mott insulator
• Quantized Rotation of Atoms From Photons with Orbital Angular Momentum
• Quantum phases in an optical lattice
• The Mott insulator transition in two dimensions
• Imaging the Mott Insulator Shells using Atomic Clock Shifts
• Formation of spatial shell structures in the superfluid to Mott insulator transition
• Bragg Spectroscopy of Vortex Lattices in Bose-Einstein condensates
• Coexistence of superfluid and Mott phases of lattice bosons

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• Low-dimensional quantum gases in curved geometries
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• First-order phase transition and anomalous hysteresis of Bose gases in optical lattices
• Confined p-band Bose-Einstein condensates
• Characteristic temperature for the immiscible-miscible transition of binary condensates in optical lattices
• Shell-shaped atomic gases
• The Inhomogeneous Extended Bose-Hubbard Model: A Mean-Field Theory
• Bose-Hubbard Models in Confining Potentials: An Inhomogeneous Mean-Field Theory
• Probing condensate order in deep optical lattices
• Signatures of the superfluid to Mott insulator transition in cold bosonic atoms in a one dimensional optical lattice
• Particle-Hole Asymmetry and Brightening of Solitons in A Strongly Repulsive BEC
• Improving Mean-Field Theory for Bosons in Optical Lattices via Degenerate Perturbation Theory
• Bose-Einstein condensates and the thin-shell limit in anisotropic bubble traps
• Finite-temperature degenerate perturbation theory for bosons in optical lattices
• Out-of-equilibrium dynamics of Bose-Bose mixtures in optical lattices
• Emergence of damped-localized excitations of the Mott state due to disorder
• The Bose-Hubbard polaron from weak to strong coupling