Stroboscopic nonlinear dynamics: a time-independent theoretical framework

TL;DR

This paper introduces a rigorous, time-independent theoretical framework for understanding and engineering stroboscopic nonlinear dynamics, which arise from time-modulated nonlinear interactions, and demonstrates its effectiveness in modeling such systems.

Contribution

The work provides the first comprehensive theoretical analysis of stroboscopic nonlinear dynamics and develops an effective time-independent model that accurately captures the phenomena.

Findings

The model nearly exactly reproduces full time-dependent dynamics in the quasi-steady state.

It significantly outperforms previous empirical descriptions.

Provides a clear physical understanding of stroboscopic nonlinear phenomena.

Abstract

Recent experiments have demonstrated the ability to manipulate nonlinear interactions via time modulation, giving rise to the so-called stroboscopic nonlinearity. To date, however, this phenomenon has not been subjected to a rigorous theoretical analysis. In this work, we elucidate the physical mechanism underlying stroboscopic nonlinear dynamics and establish an effective time-independent model under suitable modulation conditions. The proposed model almost exactly reproduces the full time-dependent dynamics in the quasi-steady state and significantly outperforms empirical descriptions used previously. Our results provide a clear physical picture of stroboscopic nonlinear dynamics and establish a general framework for engineering nonlinear interactions through temporal modulation.