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Physical Review A

Controlling directed transport of matter-wave solitons using the ratchet effect

M. Rietmann, R. Carretero-González, Ricardo Chacón

Published May 16, 2011• 33 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.83.053617

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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.
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 report on the design of a Hamiltonian ratchet exploiting periodically at rest integrable trajectories in the phase space of a modulated periodic potential, leading to the linear nondiffusive transport of particles. Using Bose-Einstein condensates in a modulated one-dimensional optical lattice, we make the first observations of this spatial ratchet, which provides way to coherently transport matter waves with possible applications in quantum technologies. In the semiclassical regime, the quantum transport strongly depends on the effective Planck constant due to Floquet state mixing. We also demonstrate the interest of quantum optimal control for efficient initial state preparation into the transporting Floquet states to enhance the transport periodicity.
We study the response of a Bose-Einstein Condensate in a δ-kicked optical lattice ratchet potential, with δ-kicked interactions, at quantum resonances. Our results reveal a strong dependency on the kicking strength K and the interaction parameter g˜. A critical curve in the (K,g˜)-space separating quasi-periodicity from full chaos shows that full chaos can be easily achieved for stronger interactions. In the full chaos regime, large currents including current reversals are generated and the current spectrum symmetry is broken. Outside the stability window, |g˜|≤1, the directed transport is no longer guaranteed. Experiments are possible thanks to recent progress in optical lattices and the possibility of time-modulating Feshbach-resonance.
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.