40 research outputs found
Dynamics of matter solitons in weakly modulated optical lattices
It is shown that matter solitons can be effectively managed by means of
smooth variations of parameters of optical lattices in which the condensate is
loaded. The phenomenon is based on the effect of lattice modulations on the
carrier wave transporting the soliton and that is why is well understood in
terms of the effective mass approach, where a particular spatial configuration
of the band structure is of primary importance. Linear, parabolic, and
spatially localized modulations are considered as the case examples. It is
shown that these defects can originate accelerating and oscillating motion of
matter solitons as well as simulate soliton interaction with attractive and
repulsive defects.Comment: 6 pages, 7 figures (text with major revision
Dynamical generation of interwoven soliton trains by nonlinear emission in binary Bose-Einstein condensates
We propose a method for the generation of trains of alternating bright
solitons in two-component Bose-Einstein condensates, using controlled emission
of nonlinear matter-waves in the uncoupled regime with spatially-varying
intra-species interaction and out-of-phase oscillations of the ground states in
the trap. Under this scheme, solitons are sequentially launched from the
different components, and interact with each other through phase-independent
cross-coupling. We obtain an analytical estimation of the critical condition
for soliton emission using a geometric guiding model, in analogy with
integrated optical systems. In addition, we show how strong initial
perturbations in the system can trigger the spontaneous generation of
supersolitons, i.e. localized phonon-like excitations of the soliton trains.
Finally, we demonstrate the controllable generation of slow and fast
supersolitons by adding external localized potentials in the nonlinear region
Defect modes of a Bose-Einstein condensate in an optical lattice with a localized impurity
We study defect modes of a Bose-Einstein condensate in an optical lattice
with a localized defect within the framework of the one-dimensional
Gross-Pitaevskii equation. It is shown that for a significant range of
parameters the defect modes can be accurately described by an expansion over
Wannier functions, whose envelope is governed by the coupled nonlinear
Schr\"{o}dinger equation with a delta-impurity. The stability of the defect
modes is verified by direct numerical simulations of the underlying
Gross-Pitaevskii equation with a periodic plus defect potentials. We also
discuss possibilities of driving defect modes through the lattice and suggest
ideas for their experimental generation.Comment: 14 pages, 9 Figures, 1 Tabl
Driving defect modes of Bose-Einstein condensates in optical lattices
We present an approximate analytical theory and direct numerical computation
of defect modes of a Bose-Einstein condensate loaded in an optical lattice and
subject to an additional localized (defect) potential. Some of the modes are
found to be remarkably stable and can be driven along the lattice by means of a
defect moving following a step-like function defined by the period of Josephson
oscillations and the macroscopic stability of the atoms.Comment: 4 pages, 5 figure
Adiabatic dynamics of periodic waves in Bose-Einstein condensate with time dependent atomic scattering length
Evolution of periodic matter waves in one-dimensional Bose-Einstein
condensates with time dependent scattering length is described. It is shown
that variation of the effective nonlinearity is a powerful tool for controlled
generation of bright and dark solitons starting with periodic waves.Comment: 4 pages, 1 figur
Nonlinear tunneling in two-dimensional lattices
We present thorough analysis of the nonlinear tunneling of Bose-Einstein
condensates in static and accelerating two-dimensional lattices within the
framework of the mean-field approximation. We deal with nonseparable lattices
considering different initial atomic distributions in the highly symmetric
states. For analytical description of the condensate before instabilities are
developed, we derive several few-mode models, analyzing both essentially
nonlinear and quasi-linear regimes of tunneling. By direct numerical
simulations, we show that two-mode models provide accurate description of the
tunneling when either initially two states are populated or tunneling occurs
between two stable states. Otherwise a two-mode model may give only useful
qualitative hints for understanding tunneling but does not reproduce many
features of the phenomenon. This reflects crucial role of the instabilities
developed due to two-body interactions resulting in non-negligible population
of the higher bands. This effect becomes even more pronounced in the case of
accelerating lattices. In the latter case we show that the direction of the
acceleration is a relevant physical parameter which affects the tunneling by
changing the atomic rates at different symmetric states and by changing the
numbers of bands involved in the atomic transfer