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

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.