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Physical Review A

Bloch oscillations in the Mott-insulator regime (4 pages)

Andrey R. Kolovsky

Published Jan 1, 2004• 1 citation
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Many-body Bloch oscillations

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We study the dynamical response of cold interacting atoms in the Mott insulator phase to a static force. As shown in the experiment by [M. Greiner et al., Nature 415, 39 (2002)], this response has resonant character, with the main resonance defined by coincidence of Stark energy and on-site interaction energy. We analyze the dynamics of the atomic momentum distribution, which is the quantity measured in the experiment, for near resonant forcing. The momentum distribution is shown to develop a recurring interference pattern, with a recurrence time which we define in the paper.
We investigate the interaction-induced superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings n=1n=1n=1, n=2n=2n=2, and n=3n=3n=3 by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.