"Bloch oscillations" in the Mott-insulator regime

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 \textbf{415}, 39 (2002), this response has resonant character, with the main resonance defined by coincidence of Stark energy and on-site interaction energy. We analyse 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.Comment: 4 pages, 5 figure

Topological phase transitions in tilted optical lattices

We analyze the energy spectrum and eigenstates of cold atoms in a tilted brick-wall optical lattice. When the tilt is applied, the system exhibits a sequence of topological phase transitions reflected in an abrupt change of the eigenstates. It is demonstrated that these topological phase transitions can be easily detected in a laboratory experiment by observing Bloch oscillations of cold atoms.Comment: 3 pages, 4 figure

On quantum phase transitions in tilted 2D lattices

We discuss the quantum phase transition from the Mott-insulator state to the density-wave state for cold Bose atoms in a 2D square lattice as the lattice is adiabatically tilted along one of its primary axes. It is shown that a small misalignment of the tilt drastically changes the result of the adiabatic passage and, instead of the density-wave state, one obtains a disordered state. Intrinsic relation of the problem to Bloch oscillations of hard-core bosons in a 2D lattice is illuminated.Comment: 4 pages, 3 figure

Persistent current of atoms in a ring optical lattice

We consider a small ensemble of Bose atoms in a ring optical lattice with weak disorder. The atoms are assumed to be initially prepared in a superfluid state with non-zero quasimomentum and, hence, may carry matter current. It is found that the atomic current persists in time for a low value of the quasimomentum but decays exponentially for a high (around one quater of the Brillouin zone) quasimomentum. The explanation is given in terms of low- and high-energy spectra of the Bose-Hubbard model, which we describe using the Bogoliubov and random matrix theories, respectively.Comment: 17 pages, IOP-styl