Excitations of Bose-Einstein condensates in optical lattices

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Abstract
In this paper we describe numerical simulations of the response of atoms confined in an optical lattice in the region of a quantum phase transition. We use the increase in the number variance of atoms as the diagnostic of excitations produced by tilting the lattice. We show that this locally determined quantity is a good indicator of the resulting coherence changes as observed in recent experiments. This is found to hold for commensurate and noncommensurate filling of the lattice, implying that our results should hold for a wide range of conditions. In accordance with this view, we find that the qualitative features of our results are in good agreement with recent experiments. We do, however, find extra features in the excitation spectra that may well be of use in future experimental studies. We also show that the variation of the spectra with the duration of the perturbation is a useful diagnostic of the atom dynamics that take place during the tilt.