140 research outputs found
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
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