Hall conductivity beyond the linear response regime

The paper introduces a semi-analytical method for calculating the Hall conductivity in the single-band approximations. The method goes beyond the linear response theory and, thus, imposes no limitation on the electric fields magnitude. It is shown that the Hall current decreases with increase of the electric field, if the Bloch frequency (which is proportional to the electric field) exceeds the cyclotron frequency (which is proportional to the magnetic field). The obtained results can be directly applied to the system of cold Bose atoms in a 2D optical lattice, where the single-band approximation is well justified.Comment: 13 pages, 4 figure

Effect of the lattice alignment on Bloch oscillations of a Bose-Einstein condensate in a square optical lattice

We consider a Bose-Einstein condensate of ultracold atoms loaded into a square optical lattice and subject to a static force. For vanishing atom-atom interactions the atoms perform periodic Bloch oscillations for arbitrary direction of the force. We study the stability of these oscillations for non-vanishing interactions, which is shown to depend on an alignment of the force vector with respect to the lattice crystallographic axes. If the force is aligned along any of the axes, the mean field approach can be used to identify the stability conditions. On the contrary, for a misaligned force one has to employ the microscopic approach, which predicts periodic modulation of Bloch oscillations in the limit of a large forcing.Comment: 4 pages, 3 figure

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 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.Comment: EPL-style, 8 pages, 4 figure

Wannier-Stark resonances in optical and semiconductor superlattices

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.Comment: 94 pages, 41 figures, typos corrected, references adde

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.Comment: submitted to the review section of IJMPB, few misprints are correcte

Dipole and Bloch oscillations of cold atoms in a parabolic lattice

The paper studies the dynamics of a Bose-Einstein condensate loaded into a 1D parabolic optical lattice, and excited by a sudden shift of the lattice center. Depending on the magnitude of the initial shift, the condensate undergoes either dipole or Bloch oscillations. The effects of dephasing and of atom-atom interactions on these oscillations are discussed.Comment: 3 pages, to appear in proceeding of LPHYS'05 conference (July 4-8, 2005, Kyoto, Japan