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arXiv:cond-mat/0312024 · Physical Review A

Bloch oscillations in the Mott-insulator regime

Andrey R. Kolovsky

Published Jul 29, 2004• 19 citations
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Abstract

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.

DOI
10.1103/physreva.70.015604

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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.
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We study a model of an equal mixture of two species of fermions in a deep optical lattice at a filling of two fermions per site. At weak interspecies interaction, the system is a band insulator. When the interspecies interaction is tuned via a Feshbach resonance to be larger than an energy related to the energy separation of the first and second Bloch bands, atoms populate equally the two Bloch bands. With weak tunneling between sites of the optical lattice, the system becomes a Mott insulator with the low-energy effective Hamiltonian of a spin-1 Heisenberg antiferromagnet, because of a Hund's-rule-like coupling between the two bands. We discuss experimental signatures of these two types of insulators.
We analyze theoretically the experiment reported in [F. Gerbier et al., Phys. Rev. Lett. 95, 050404 (2005)]. There, the interference pattern produced by an expanding atomic cloud in the Mott insulator regime was observed, indicative of short-range coherence in the system. The latter was traced back to the presence of a small amount of particle-hole pairs in the insulating phase for finite lattice depths. We analyze the influence of these pairs on the interference pattern using a random phase approximation, and derive the corresponding visibility. We also account for the inhomogeneity inherent to atom traps in a local density approximation. The calculations reproduce the experimental observations, except for very large lattice depths. The deviation from the measurement in this range is attributed to the increasing importance of nonadiabatic effects.
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The response of ultracold atomic Bose gases in time-dependent optical lattices is discussed based on direct simulations of the time-evolution of the many-body state in the framework of the Bose-Hubbard model. We focus on small-amplitude modulations of the lattice potential as implemented in several recent experiments and study different observables in the region of the first resonance in the Mott-insulator phase. In addition to the energy transfer we investigate the quasimomentum structure of the system which is accessible via the matter-wave interference pattern after a prompt release. We identify characteristic correlations between the excitation frequency and the quasimomentum distribution and study their structure in the presence of a superlattice potential.