317 research outputs found
Dynamics of matter-wave solitons in a ratchet potential
We study the dynamics of bright solitons formed in a Bose-Einstein condensate
with attractive atomic interactions perturbed by a weak bichromatic optical
lattice potential. The lattice depth is a biperiodic function of time with a
zero mean, which realises a flashing ratchet for matter-wave solitons. The
average velocity of a soliton and the directed soliton current induced by the
ratchet depend on the number of atoms in the soliton. We employ this feature to
study collisions between ratchet-driven solitons and find that soliton
transport can be induced through their interactions. In the regime when
matter-wave solitons are narrow compared to the lattice period the ratchet
dynamics is well described by the effective Hamiltonian theory.Comment: 4 pages, 5 figure
Asymmetric vortex solitons in nonlinear periodic lattices
We reveal the existence of asymmetric vortex solitons in ideally symmetric
periodic lattices, and show how such nonlinear localized structures describing
elementary circular flows can be analyzed systematically using the
energy-balance relations. We present the examples of rhomboid, rectangular, and
triangular vortex solitons on a square lattice, and also describe novel
coherent states where the populations of clockwise and anti-clockwise vortex
modes change periodically due to a nonlinearity-induced momentum exchange
through the lattice. Asymmetric vortex solitons are expected to exist in
different nonlinear lattice systems including optically-induced photonic
lattices, nonlinear photonic crystals, and Bose-Einstein condensates in optical
lattices.Comment: 4 pages, 5 figure
Self-trapped nonlinear matter waves in periodic potentials
We demonstrate that the recent observation of nonlinear self-trapping of matter waves in one-dimensional optical lattices [Th. Anker et al., Phys. Rev. Lett. 94, 020403 (2005)] can be associated with a novel type of broad nonlinear state existing in the gaps of the matter-wave band-gap spectrum. We find these self-trapped localized modes in one-, two-, and three-dimensional periodic potentials, and demonstrate that such novel gap states can be generated experimentally in any dimension
Matter Waves in Anharmonic Periodic Potentials
We study anharmonic (optical or magnetic) periodic potentials and demonstrate that they may exhibit unusual features in the band-gap spectra and the nature of the matter-wave Bloch waves and solitons. We reveal that the band gaps may be strongly modifie
Melting of Discrete Vortices via Quantum Fluctuations
We consider nonlinear boson states with a nontrivial phase structure in the
three-site Bose-Hubbard ring, {\em quantum discrete vortices} (or {\em
q-vortices}), and study their "melting" under the action of quantum
fluctuations. We calculate the spatial correlations in the ground states to
show the superfluid-insulator crossover and analyze the fidelity between the
exact and variational ground states to explore the validity of the classical
analysis. We examine the phase coherence and the effect of quantum fluctuations
on q-vortices and reveal that the breakdown of these coherent structures
through quantum fluctuations accompanies the superfluid-insulator crossover.Comment: Revised version, 4 pages, 5 figures, Accepted for publication in
Physical Review Letter
Multi-component gap solitons in spinor Bose-Einstein condensates
We model the nonlinear behaviour of spin-1 Bose-Einstein condensates (BECs)
with repulsive spin-independent interactions and either ferromagnetic or
anti-ferromagnetic (polar) spin-dependent interactions, loaded into a
one-dimensional optical lattice potential. We show that both types of BECs
exhibit dynamical instabilities and may form spatially localized
multi-component structures. The localized states of the spinor matter waves
take the form of vector gap solitons and self-trapped waves that exist only
within gaps of the linear Bloch-wave band-gap spectrum. Of special interest are
the nonlinear localized states that do not exhibit a common spatial density
profile shared by all condensate components, and consequently cannot be
described by the single mode approximation (SMA), frequently employed within
the framework of the mean-field treatment. We show that the non-SMA states can
exhibits Josephson-like internal oscillations and self-magnetisation, i.e.
intrinsic precession of the local spin. Finally, we demonstrate that
non-stationary states of a spinor BEC in a lattice exhibit coherent undamped
spin-mixing dynamics, and that their controlled conversion into a stationary
state can be achieved by the application of an external magnetic field.Comment: 12 pages, 13 figure
Spatial Optical Solitons due to Multistep Cascading
We introduce a novel class of parametric optical solitons supported
simultaneously by two second-order nonlinear cascading processes,
second-harmonic generation and sum-frequency mixing. We obtain, analytically
and numerically, the solutions for three-wave spatial solitons and show that
the presence of an additional cascading mechanism can change dramatically the
properties and stability of two-wave quadratic solitary waves.Comment: 6 pages, 4 figure
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