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note
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The condition γ = 1 / 3, 1 / 2 can be realized by choosing λ ≈ 764 nm, 762 nm, respectively. These values of the lattice wavelength are, however, rather close to the atomic resonances, where a substantial heating effect from photon scattering is expected. This could make the experimental observation more difficult on long time scales.
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e-print arXiv: 1007.3828, for mixtures of fermions and bosons in different optical lattices where tilting of the lattice for fermions was considered.
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During the completion of this work, we became aware that similar expressions for the matrix elements M in Eq. (22) have been very recently derived independently in M. Bruderer, T. H. Johnson, S. R. Clark, D. Jaksch, A. Posazhennikova, and W. Belzig, e-print arXiv: 1007.3828, for mixtures of fermions and bosons in different optical lattices where tilting of the lattice for fermions was considered.
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During the Completion of This Work, We Became Aware That Similar Expressions for the Matrix Elements M in Eq. (22) Have Been Very Recently Derived Independently
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Bruderer, M.1
Johnson, T.H.2
Clark, S.R.3
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Posazhennikova, A.5
Belzig, W.6
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