Abstract

We study the rectification process of interacting quantum particles in a periodic potential exposed to the action of an external ac driving. The breaking of spatio-temporal symmetries leads to directed motion even in the absence of interactions. A hallmark of quantum ratcheting is the appearance of resonant enhancement of the current (Denisov et al 2007 Europhys. Lett. 79 10007; Denisov et al 2007 Phys. Rev. A 75 063424). Here, we study the fate of these resonances within a Gross–Pitaevskii equation which describes a mean field interaction between many particles. We find that the resonance (i) is not destroyed by interactions, (ii) shifts its location with increasing interaction strength. We trace the Floquet states of the linear equations into the nonlinear domain, and show that the resonance gives rise to an instability and thus to the appearance of new nonlinear Floquet states, whose transport properties differ strongly as compared to the case of noninteracting particles.