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n is the nth-order Bessel function, and T is the tunneling matrix element between lattice sites. See, G. Wannier, Phys. Rev. 117, 432 (1961); H. Fukuyama, R. Bari, H. Fogedby, Phys. Rev. B 8, 5579 (1973); D. Emin and C. Hart, ibid. 36, 7353 (1987).
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n is the nth-order Bessel function, and T is the tunneling matrix element between lattice sites. See, G. Wannier, Phys. Rev. 117, 432 (1961); H. Fukuyama, R. Bari, H. Fogedby, Phys. Rev. B 8, 5579 (1973); D. Emin and C. Hart, ibid. 36, 7353 (1987).
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n is the nth-order Bessel function, and T is the tunneling matrix element between lattice sites. See, G. Wannier, Phys. Rev. 117, 432 (1961); H. Fukuyama, R. Bari, H. Fogedby, Phys. Rev. B 8, 5579 (1973); D. Emin and C. Hart, ibid. 36, 7353 (1987).
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3643109912
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note
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q is offset by an arbitrary factor from the local lattice minimum. Because this offset is identical for each well, it amounts to a trivial spatial shift in the interference pattern.
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22
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3643118238
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note
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Numerical solutions to the nonlinear Schrödinger equation indicate an oscillation amplitude of a few lattice sites for parameters used in our experiments.
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3643056652
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th > 1. We inferred the temperature, T, from the spatial expansion of a pulse during the observation interval, and density, n, from the observed optical depth and spatial extent of the pulse (Fig. 4).
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39
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3643082861
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note
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Note that turning on the optical potential adiabatically takes the condensate from the Thomas-Fermi regime (lattice potential off), where mean-field interaction energy dominates kinetic energy, to a regime where kinetic energy dominates the mean-field energy (lattice potential on).
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40
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3643053499
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note
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We thank M. Yasuda for technical assistance. Supported by the NSF and the Office of Naval Research.
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