7 research outputs found
Transport behaviour of a Bose Einstein condensate in a bichromatic optical lattice
The Bloch and dipole oscillations of a Bose Einstein condensate (BEC) in an
optical superlattice is investigated. We show that the effective mass increases
in an optical superlattice, which leads to localization of the BEC, in
accordance with recent experimental observations [16]. In addition, we find
that the secondary optical lattice is a useful additional tool to manipulate
the dynamics of the atoms.Comment: Modified manuscrip
Black soliton in a quasi-one-dimensional trapped fermion-fermion mixture
Employing a time-dependent mean-field-hydrodynamic model we study the
generation of black solitons in a degenerate fermion-fermion mixture in a
cigar-shaped geometry using variational and numerical solutions. The black
soliton is found to be the first stationary vibrational excitation of the
system and is considered to be a nonlinear continuation of the vibrational
excitation of the harmonic oscillator state. We illustrate the stationary
nature of the black soliton, by studying different perturbations on it after
its formation.Comment: 7 pages, 10 figure
Surface Gap Soliton Ground States for the Nonlinear Schr\"{o}dinger Equation
We consider the nonlinear Schr\"{o}dinger equation , with and and with periodic in each coordinate direction. This problem
describes the interface of two periodic media, e.g. photonic crystals. We study
the existence of ground state solutions (surface gap soliton ground
states) for . Using a concentration compactness
argument, we provide an abstract criterion for the existence based on ground
state energies of each periodic problem (with and ) as well as a more practical
criterion based on ground states themselves. Examples of interfaces satisfying
these criteria are provided. In 1D it is shown that, surprisingly, the criteria
can be reduced to conditions on the linear Bloch waves of the operators
and .Comment: definition of ground and bound states added, assumption (H2) weakened
(sign changing nonlinearity is now allowed); 33 pages, 4 figure
Modulated Amplitude Waves in Bose-Einstein Condensates
We analyze spatio-temporal structures in the Gross-Pitaevskii equation to
study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs)
with mean-field interactions. A coherent structure ansatz yields a
parametrically forced nonlinear oscillator, to which we apply Lindstedt's
method and multiple-scale perturbation theory to determine the dependence of
the intensity of periodic orbits (``modulated amplitude waves'') on their wave
number. We explore BEC band structure in detail using Hamiltonian perturbation
theory and supporting numerical simulations.Comment: 5 pages, 4 figs, revtex, final form of paper, to appear in PRE
(forgot to include \bibliography command in last update, so this is a
correction of that; the bibliography is hence present again
Many particle entanglement in two-component Bose-Einstein Condensates
We investigate schemes to dynamically create many particle entangled states
of a two component Bose-Einstein condensate in a very short time proportional
to 1/N where is the number of condensate particles. For small we
compare exact numerical calculations with analytical semiclassical estimates
and find very good agreement for . We also estimate the effect of
decoherence on our scheme, study possible scenarios for measuring the entangled
states, and investigate experimental imperfections.Comment: 12 pages, 8 figure