Nonlinearity-induced localization in a periodically-driven semi-discrete system

TL;DR

This paper shows that nonlinearity can induce and support robust dynamical localization in a semi-discrete system with periodic driving, contrasting the delocalization observed in the linear regime.

Contribution

It reveals that cubic nonlinearity induces stable localization in a semi-discrete system under periodic modulation, a novel finding in nonlinear dynamical systems.

Findings

Nonlinearity induces robust localization of wave packets.

Periodic modulation causes delocalization in the linear regime.

Localization persists under combined static and oscillating potentials.

Abstract

We demonstrate that nonlinearity plays a constructive role in supporting the robustness of dynamical localization in a model which is discrete, in one dimension and continuous in the orthogonal one. In the linear regime, time-periodic modulation of the gradient strength along the discrete axis leads to the usual rapid spread of an initially confined wave packet. Addition of the cubic nonlinearity makes the dynamics drastically different, inducing robust localization of moving wave packets. Similar nonlinearity-induced effects are also produced by combinations of static and oscillating linear potentials. The predicted nonlinearity-induced dynamical localization can be realized in photonic lattices and Bose-Einstein condensates.