Nonlinear wave-packet dynamics resonantly driven by AC and DC fields

The dynamics of a charged single-particle placed in a chain under the simultaneous action of local non-linearity and superposed harmonic AC and static fields (DC field) is considered. The non-linearity is represented as a diagonal potential proportional to the square modulus of the local wave-function. We unveil a rich dynamics with the wave-packet fronts displaying either a continuous spreading or a solitonic-like evolution depending on a delicate balance between the non-linearity strength and the phase of an AC field in resonance with the Bloch oscillations induced by a DC field. In particular, the non-linearity induces a unidirectional motion of the wave-packet centroid of an initially fully localized wave-packet which is absent in the linear regime.