Asymmetric Floquet-Engineered Mode Coupling in Hybrid Magnonics

In hybrid magnonic systems, linear magnon--photon hybridization inherently produces symmetric, reciprocal interactions, precluding asymmetric mode coupling. Floquet driving can tailor mode coupling strengths but, with single-tone modulation, inevitably generates a symmetric interaction that preserves this reciprocity. Here we introduce dual-tone Floquet modulation to unlock a new degree of freedom in hybrid magnonic systems, where the relative phase $\theta$ of two commensurate drives continuously controls the asymmetry of the Floquet-engineered interaction, enabling asymmetric mode coupling absent in existing hybrid magnonic systems. We demonstrate this in a strongly coupled cavity magnonic device, where tuning $\theta$ reversibly switches single-sided Autler--Townes splitting between the two hybrid modes---a direct spectroscopic signature of phase-programmable asymmetric coupling. This approach opens a new path toward controllable nonreciprocal and topological functionalities in hybrid magnonic systems, with broad implications for advanced quantum and classical signal processing.