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