Delocalization and spreading in a nonlinear Stark ladder

We study the evolution of a wave packet in a nonlinear Stark ladder. In the absence of nonlinearity all normal modes are spatially localized giving rise to an equidistant eigenvalue spectrum and Bloch oscillations. Nonlinearity induces frequency shifts and mode-mode interactions and destroys localization. For large strength of nonlinearity we observe single-site trapping as a transient, with subsequent explosive spreading, followed by subdiffusion. For moderate nonlinearities an immediate subdiffusion takes place. Finally, for small nonlinearities we find linear Stark localization as a transient, with subsequent subdiffusion. For single-mode excitations and weak nonlinearities, stability intervals are predicted and observed upon variation in the dc bias strength, which affects the short- and the long-time dynamics.