"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

Bright solitons and self-trapping with a BEC of cold atoms in driven tilted optical lattices

We suggest a method for creating bright matter solitons by loading a BEC of atoms in a driven tilted optical lattice. It is shown that one can realize the self-focussing regime for the wave-packet dynamics by properly adjusting the phase of the driving field with respect to the phase of Bloch oscillations. If atom-atom interactions are larger than some critical value $g_{min}$, this self-focussing regime is followed by the formation of bright solitons. Increasing the interactions above another critical value $g_{max}$ makes this process unstable. Instead of soliton formation one now meets the phenomenon of incoherent self-trapping. In this regime a fraction of atoms is trapped in incoherent localized wave-packets, while the remaining atoms spread ballistically.Comment: 4 pages, 4 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

Landau-Stark states and cyclotron-Bloch oscillations of a quantum particle

Recent experimental progress in the creation of synthetic electric and magnetic fields, acting on cold atoms in a two-dimensional lattice, has attracted renewed interest to the problem of a quantum particle in the Hall configuration. The present work contains a detailed analysis of the eigenstates of this system, called Landau-Stark states, and of the associated dynamical phenomenon of cyclotron-Bloch oscillations. It is shown that Landau-Stark states and cyclotron-Bloch oscillations crucially depend on two factors. The first is the orientation of the electric field relative to the primary axes of the lattice. The second is ratio between the frequencies of Bloch and cyclotron oscillations, that is also the ratio between the magnitudes of electric and magnetic fields. The analysis is first carried out in the tight-binding approximation, where the magnetic field is characterized by the Peierls phase entering the hopping matrix elements. Agreement of this analysis with the full quantum theory is also studied.Comment: 39 pages, 26 figure

Master equation approach to conductivity of bosonic and fermionic carriers in one- and two-dimensional lattices

We discuss the master equation approach to diffusive current of bosonic or fermionic carriers in one- and two-dimensional lattices. This approach is shown to reproduce all known results of the linear response theory, including the integer quantum Hall effect for fermionic carriers. The main advantage of the approach is that it allows to calculate the current beyond the linear response regime where new effects are found. In particular, we show that the Hall current can be inverted by changing orientation of the static force (electric field) relative to the primary axes of the lattice.Comment: 22 pages, 9 figure