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We note here that while in our experiment J is changed through V0 (which has little effect on U in the range of parameters used here), in the numerical simulation J is kept constant and U is varied. The latter situation could be exactly reproduced experimentally by using a Feshbach resonance. The agreement between our experimental results and the simulation indicates that it is the ratio U/J rather than the two individual parameters that governs the system's behavior.
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We note here that while in our experiment J is changed through V0 (which has little effect on U in the range of parameters used here), in the numerical simulation J is kept constant and U is varied. The latter situation could be exactly reproduced experimentally by using a Feshbach resonance. The agreement between our experimental results and the simulation indicates that it is the ratio U/J rather than the two individual parameters that governs the system's behavior.
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In the 1D experiments we checked that the trap modulation in the direction perpendicular to the tubes (i.e., in the direction of the 2D lattice) did not lead to an excitation of the Bose gas for any value of the lattice depth of the 1D lattice. This was done by modulating only the dipole trap beam that was approximately collinear with the 1D lattice beam and checking the response of the Bose gas as a function of V0.
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In the 1D experiments we checked that the trap modulation in the direction perpendicular to the tubes (i.e., in the direction of the 2D lattice) did not lead to an excitation of the Bose gas for any value of the lattice depth of the 1D lattice. This was done by modulating only the dipole trap beam that was approximately collinear with the 1D lattice beam and checking the response of the Bose gas as a function of V0.
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Deviations from the mean-field thresholds are discussed in.
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