Delocalization and spreading in a nonlinear Stark ladder

TL;DR

This paper investigates how nonlinearity affects wave packet evolution in a Stark ladder, revealing transient localization, subdiffusion, and explosive spreading phenomena in a nonlinear Schrödinger lattice with a dc bias.

Contribution

It provides a detailed analysis of the nonlinear dynamics in a Stark ladder, highlighting the transition from localization to subdiffusion and explosive spreading due to mode interactions.

Findings

Localization as a transient with subdiffusion at higher nonlinearity

Immediate subdiffusion caused by strong mode interactions

Transient single-site trapping followed by explosive spreading

Abstract

We study the evolution of a wave packet in a nonlinear Schr\"odinger lattice equation subject to a dc bias. In the absence of nonlinearity all normal modes are spatially localized giving rise to a Stark ladder with an equidistant eigenvalue spectrum and Bloch oscillations. Nonlinearity induces frequency shifts and mode-mode interactions and destroys localization. With increasing strength of nonlinearity we observe: (I) localization as a transient, with subsequent subdiffusion (weak mode-mode interactions); (II) immediate subdiffusion (strong mode-mode interactions); (III) single site trapping as a transient, with subsequent explosive spreading, followed by subdiffusion. For single mode excitations and weak nonlinearities stability intervals are predicted and observed upon variation of the dc bias strength, which affect the short and long time dynamics.