512 research outputs found
Dynamics and Manipulation of Matter-Wave Solitons in Optical Superlattices
We analyze the existence and stability of bright, dark, and gap matter-wave
solitons in optical superlattices. Then, using these properties, we show that
(time-dependent) ``dynamical superlattices'' can be used to controllably place,
guide, and manipulate these solitons. In particular, we use numerical
experiments to displace solitons by turning on a secondary lattice structure,
transfer solitons from one location to another by shifting one superlattice
substructure relative to the other, and implement solitonic ``path-following'',
in which a matter wave follows the time-dependent lattice substructure into
oscillatory motion.Comment: 6 pages, revtex, 6 figures, to appear in Physics Letters A; minor
modifications from last versio
Families of Matter-Waves for Two-Component Bose-Einstein Condensates
We produce several families of solutions for two-component nonlinear
Schr\"{o}dinger/Gross-Pitaevskii equations. These include domain walls and the
first example of an antidark or gray soliton in the one component, bound to a
bright or dark soliton in the other. Most of these solutions are linearly
stable in their entire domain of existence. Some of them are relevant to
nonlinear optics, and all to Bose-Einstein condensates (BECs). In the latter
context, we demonstrate robustness of the structures in the presence of
parabolic and periodic potentials (corresponding, respectively, to the magnetic
trap and optical lattices in BECs).Comment: 6 pages, 4 figures, EPJD in pres
Nonlinear localized modes in two-dimensional electrical lattices
We report the observation of spontaneous localization of energy in two
spatial dimensions in the context of nonlinear electrical lattices. Both
stationary and traveling self-localized modes were generated experimentally and
theoretically in a family of two-dimensional square, as well as hon- eycomb
lattices composed of 6x6 elements. Specifically, we find regions in driver
voltage and frequency where stationary discrete breathers, also known as
intrinsic localized modes (ILM), exist and are stable due to the interplay of
damping and spatially homogeneous driving. By introduc- ing additional
capacitors into the unit cell, these lattices can controllably induce traveling
discrete breathers. When more than one such ILMs are experimentally generated
in the lattice, the interplay of nonlinearity, discreteness and wave
interactions generate a complex dynamics wherein the ILMs attempt to maintain a
minimum distance between one another. Numerical simulations show good agreement
with experimental results, and confirm that these phenomena qualitatively carry
over to larger lattice sizes.Comment: 5 pages, 6 figure
Exploring Vortex Dynamics in the Presence of Dissipation: Analytical and Numerical Results
In this paper, we systematically examine the stability and dynamics of
vortices under the effect of a phenomenological dissipation used as a
simplified model for the inclusion of the effect of finite temperatures in
atomic Bose-Einstein condensates. An advantage of this simplified model is that
it enables an analytical prediction that can be compared directly (and
favorably) to numerical results. We then extend considerations to a case of
considerable recent experimental interest, namely that of a vortex dipole and
observe good agreement between theory and numerical computations in both the
stability properties (eigenvalues of the vortex dipole stationary states) and
the dynamical evolution of such configurations.Comment: 12 pages, 5 figures, accepted by PR
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