Phase control of localization in the nonlinear two-mode system from harmonic mixing driving: Perturbative analysis and symmetry consideration

TL;DR

This paper offers a detailed perturbative analysis of symmetry effects in a nonlinear two-mode system driven by harmonic mixing, elucidating how these symmetries influence localization and dynamical behavior, with applications in Bose-Einstein condensates and nonlinear optics.

Contribution

It provides a rigorous symmetry-based analysis using perturbation theory to understand phase control in nonlinear two-mode systems driven by harmonic mixing.

Findings

Symmetries significantly influence the system's dynamical features.

Effective second-order perturbation accurately predicts Floquet spectra.

Results are applicable to atomic localization and optical signal switching.

Abstract

In this paper, we present a rigorous analysis of symmetry and underlying physics of the nonlinear two-mode system driven by a harmonic mixing field, by means of multiple scale asymptotic analysis method. The effective description in the framework of the second-order perturbative theory provides an accurate picture for understanding the Floquet eigenspectrum and dynamical features of the nonlinear two-mode system, showing full agreement with the prediction of symmetry considerations. We find that two types of symmetries play significant role in the dynamical features of this model, the mechanism behind which can be interpreted in terms of the effective description. The results are of relevance for the phase control of the atomic localization in Bose-Einstein condensates or switch of the optical signals in nonlinear mediums.