Semi-Analytical Engineering of Strongly Driven Nonlinear Systems Beyond Floquet and Perturbation Theory

TL;DR

This paper introduces a semi-analytical, non-perturbative framework that extends Floquet theory to nonlinear systems, enabling precise control and engineering of strongly driven nonlinear dynamics beyond traditional methods.

Contribution

The work develops a heuristic extension of Floquet theory combined with a novel constrained optimization technique for better control of nonlinear systems.

Findings

Effective potential engineering across broader parameter spaces

Enhanced control of nonclassical states and quantum simulations

Applicable to diverse experimental platforms

Abstract

Strongly driven nonlinear systems are frequently encountered in physics, yet their accurate control is generally challenging due to the intricate dynamics. In this work, we present a non-perturbative, semi-analytical framework for tailoring such systems. The key idea is heuristically extending the Floquet theory to nonlinear differential equations using the Harmonic Balance method. Additionally, we establish a novel constrained optimization technique inspired by the Lagrange multiplier method. This approach enables accurate engineering of effective potentials across a broader parameter space, surpassing the limitations of perturbative methods. Our method offers practical implementations in diverse experimental platforms, facilitating nonclassical state generation, versatile bosonic quantum simulations, and solving complex optimization problems across quantum and classical applications.