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Quantum Electronics and Laser Science Conference

Ultra cold bosons in incommensurate optical lattices

Nir Bar‐Gill, Rami Pugatch, Eitan E. Rowen, Nir Davidson

Published May 1, 2007• 1 citation
Publisher

Abstract

We study the quantum phase diagram of ultra cold bosons in 1D incommensurate optical lattices, as compared to commensurate lattices. We also examine the experimental implications of incommesurability and one spatial dimension.
DOI
10.1109/qels.2007.4431785

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We study cold atomic gases with a contact interaction and confined into one-dimension. Crossing the confinement induced resonance the correlation between the bosons increases, and introduces an effective range for the interaction potential. Using the mapping onto the sine-Gordon model and a Hubbard model in the strongly interacting regime allows us to derive the phase diagram in the presence of an optical lattice. We find the appearance of a phase transition from a Luttinger liquid with algebraic correlations into a crystalline phase with a particle on every second lattice site.
Quantum phases and phase transitions of weakly to strongly interacting bosonic atoms in deep to shallow optical lattices are described by a single multiorbital mean-field approach in real space. For weakly interacting bosons in one dimension, the critical value of the superfluid to Mott insulator (MI) transition found is in excellent agreement with many-body treatments of the Bose-Hubbard model. For strongly interacting bosons, (i) additional MI phases appear, for which two (or more) atoms residing in each site undergo a Tonks-Girardeau-like transition and localize, and (ii) on-site excitation becomes the excitation lowest in energy. Experimental implications are discussed.