Andrey R. Kolovsky

Wannier-Stark Resonances in optical and semiconductor superlattices

Abstract In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally, this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as the Wannier–Stark problem. We describe a novel approach to the Wannier–Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier–Stark system as the poles of a rigorously constructed scattering matrix and solves the Wannier–Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier–Stark resonances appearing in different physical systems such as optical lattices or semiconductor superlattices.

Creating artificial magnetic fields for cold atoms by photon-assisted tunneling

This paper proposes a simple setup for introducing an artificial magnetic field for neutral atoms in 2D optical lattices. This setup is based on the phenomenon of photon-assisted tunneling and involves a low-frequency periodic driving of the optical lattice. This low-frequency driving does not affect the electronic structure of the atom and can be easily realized by the same means which are employed to create the lattice. We also address the problem of detecting this effective magnetic field. In particular, we study the center-of-mass wave packet dynamics, which is shown to exhibit certain features of cyclotron dynamics of a classical charged particle.

Interaction-Induced Decoherence of Atomic Bloch Oscillations

We show that the energy spectrum of the Bose-Hubbard model amended by a static field exhibits Wigner-Dyson level statistics. In itself a characteristic signature of quantum chaos, this induces the irreversible decay of Bloch oscillations of cold, interacting atoms loaded into an optical lattice, and provides a Hamiltonian model for interaction-induced decoherence.

Quantum chaos in the Bose-Hubbard model

We present a numerical study of the spectral properties of the 1D Bose-Hubbard model. Unlike the 1D Hubbard model for fermions, this system is found to be non-integrable, and exhibits Wigner-Dyson spectral statistics under suitable conditions.

Atomic current across an optical lattice.

We devise a microscopic model for the emergence of a collision-induced, fermionic atomic current across a tilted optical lattice. Tuning the--experimentally controllable--parameters of the microscopic dynamics allows us to switch from Ohmic to negative differential conductance.

BLOCH OSCILLATIONS OF COLD ATOMS IN OPTICAL LATTICES

This work is devoted to Bloch oscillations (BO) of cold neutral atoms in optical lattices. After a general introduction to the phenomenon of BO and its realization in optical lattices, we study different extentions of this problem, which account for recent developments in this field. These are two-dimensional BO, decoherence of BO, and BO in correlated systems. Although these problems are discussed in relation to the system of cold atoms in optical lattices, many of the results are of general validity and can be well applied to other systems showing the phenomenon of BO.

On the spectrum of the system of interacting quantum nonlinear resonances

Abstract Correlation functions of the density matrix components and the frequency spectrum are numerically analysed in the system of two interacting quantum nonlinear resonances. For overlapping resonances and a sufficiently large number of resonance-trapped levels the motion of the system is shown to be close to stochasticity.

Semiclassical quantization of the Bogoliubov spectrum.

We analyze the Bogoliubov spectrum of the three-site Bose-Hubbard model with a finite number of Bose particles by using a semiclassical approach. The Bogoliubov spectrum is shown to be associated with the low-energy regular component of the classical Hubbard model. We identify the full set of the integrals of motion of this regular component and, quantizing them, obtain the energy levels of the quantum system. The critical values of the energy, above which the regular Bogoliubov spectrum evolves into a chaotic spectrum, is indicated as well.

Bose-Einstein condensates on tilted lattices: Coherent, chaotic, and subdiffusive dynamics

The dynamics of a (quasi-) one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schroedinger equation. If the static field is varied, the system shows a plethora of dynamical phenomena. In the strong field limit, we demonstrate the existence of (almost) nonspreading states which remain localized on the lattice region populated initially and show coherent Bloch oscillations with fractional revivals in the momentum space (so-called quantum carpets). With decreasing field, the dynamics becomes irregular, however, still confined in configuration space. For even weaker fields, we find subdiffusive dynamics with a wave-packet width growing as t{sup 1/4}.

Damped Bloch oscillations of cold atoms in optical lattices

The paper studies Bloch oscillations of cold neutral atoms in the optical lattice. The effect of spontaneous emission on the dynamics of the system is analyzed both analytically and numerically. The spontaneous emission is shown to cause (i) the decay of Bloch oscillations with the decrement given by the rate of spontaneous emission and (ii) the diffusive spreading of the atoms with a diffusion coefficient depending on both the rate of spontaneous emission and the Bloch frequency.