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Physica D Nonlinear Phenomena

Ratchet-induced matter–wave transport and soliton collisions in Bose–Einstein condensates

Dario Poletti, Elena A. Ostrovskaya, Tristram J. Alexander, Baowen Li, Yuri S. Kivshar

Published Oct 18, 2008• 19 citations
Publisher
DOI
10.1016/j.physd.2008.10.003

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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 realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory.
We demonstrate that directed transport of bright solitons formed in a quasi-one-dimensional Bose-Einstein condensate can be reliably controlled by tailoring a weak optical lattice potential, biharmonic in both space and time, in accordance with the degree of symmetry breaking mechanism. By considering the regime where matter-wave solitons are narrow compared to the lattice period, (i) we propose an analytical estimate for the dependence of the directed soliton current on the biharmonic potential parameters that is in good agreement with numerical experiments, and (ii) we show that the dependence of the directed soliton current on the number of atoms is a consequence of the ratchet universality.
For a one-dimensional nonautonomous Gross–Pitaevskii system with biperiodically driven interatom interaction and external parabolic potential which satisfy the compatibility conditions (Serkin et al 2007 Phys. Rev. Lett. 98 074102), we derive a set of exact deformed-soliton solutions with amplitudes deviated from the standard hyperbolic-secant form, which describes different single-soliton characteristics of an attractive Bose–Einstein condensate. By defining a deformation factor adjusted by the number of condensed atoms, we find that the analytical height, width, position and velocity of the deformed soliton are controlled by the deformation factor. It is numerically shown that for asymmetric sawtooth driving the temporal ratchet effect can be induced or suppressed, even reversed, by adjusting the factor. The results offer a means of experimentally manipulating directed transports of the nonautonomous solitons.