13 research outputs found
Scaling property of the critical hopping parameters for the Bose-Hubbard model
Recently precise results for the boundary between the Mott insulator phase
and the superfluid phase of the homogeneous Bose-Hubbard model have become
available for arbitrary integer filling factor g and any lattice dimension d >
1. We use these data for demonstrating that the critical hopping parameters
obey a scaling relationship which allows one to map results for different g
onto each other. Unexpectedly, the mean-field result captures the dependence of
the exact critical parameters on the filling factor almost fully. We also
present an approximation formula which describes the critical parameters for d
> 1 and any g with high accuracy.Comment: 5 pages, 5 figures. to appear in EPJ
Theoretical analysis of quantum dynamics in 1D lattices: Wannier-Stark description
This papers presents a formalism describing the dynamics of a quantum
particle in a one-dimensional tilted time-dependent lattice. The description
uses the Wannier-Stark states, which are localized in each site of the lattice
and provides a simple framework leading to fully-analytical developments.
Particular attention is devoted to the case of a time-dependent potential,
which results in a rich variety of quantum coherent dynamics is found.Comment: 8 pages, 6 figures, submitted to PR
Theoretical Analysis of a Large Momentum Beamsplitter using Bloch Oscillations
In this paper, we present the implementation of Bloch oscillations in an
atomic interferometer to increase the separation of the two interfering paths.
A numerical model, in very good agreement with the experiment, is developed.
The contrast of the interferometer and its sensitivity to phase fluctuations
and to intensity fluctuations are also calculated. We demonstrate that the
sensitivity to phase fluctuations can be significantly reduced by using a
suitable arrangement of Bloch oscillations pulses
Holstein polarons in a strong electric field: delocalized and stretched states
The coherent dynamics of a Holstein polaron in strong electric fields is
considered under different regimes. Using analytical and numerical analysis, we
show that even for small hopping constant and weak electron-phonon interaction,
the original discrete Wannier-Stark (WS) ladder electronic states are each
replaced by a semi-continuous band if a resonance condition is satisfied
between the phonon frequency and the ladder spacing. In this regime, the
original localized WS states can become {\em delocalized}, yielding both
`tunneling' and `stretched' polarons. The transport properties of such a system
would exhibit a modulation of the phonon replicas in typical tunneling
experiments. The modulation will reflect the complex spectra with
nearly-fractal structure of the semi-continuous band. In the off-resonance
regime, the WS ladder is strongly deformed, although the states are still
localized to a degree which depends on the detuning: Both the spacing between
the levels in the deformed ladder and the localization length of the resulting
eigenfunctions can be adjusted by the applied electric field. We also discuss
the regime beyond small hopping constant and weak coupling, and find an
interesting mapping to that limit via the Lang-Firsov transformation, which
allows one to extend the region of validity of the analysis.Comment: 10 pages, 13 figures, submitted to PR
Momentum state engineering and control in Bose-Einstein condensates
We demonstrate theoretically the use of genetic learning algorithms to
coherently control the dynamics of a Bose-Einstein condensate. We consider
specifically the situation of a condensate in an optical lattice formed by two
counterpropagating laser beams. The frequency detuning between the lasers acts
as a control parameter that can be used to precisely manipulate the condensate
even in the presence of a significant mean-field energy. We illustrate this
procedure in the coherent acceleration of a condensate and in the preparation
of a superposition of prescribed relative phase.Comment: 9 pages incl. 6 PostScript figures (.eps), LaTeX using RevTeX,
submitted to Phys. Rev. A, incl. small modifications, some references adde