Nonreciprocal Bistability in Coupled Nonlinear Cavity Magnonics

We propose a coupled nonlinear cavity-magnon system, consisting of two cavities, a second-order nonlinear element, and a yttrium-iron-garnet (YIG) sphere that supports Kerr magnons, to realize the sought-after highly tunable nonreciprocity. We first derive the critical condition for switching between reciprocity and nonreciprocity in the absence of magnon driving, and then numerically demonstrate that strong magnonic nonreciprocity can be achieved by violating this critical condition. When magnons are driven, we show that strong magnonic nonreciprocity can also be attained even within the critical condition. Compared to previous studies, the introduced nonlinear element not only relaxes the critical condition in both the weak and strong coupling regimes, but also offers an alternative means to tune magnonic nonreciprocity. Our work provides a promising avenue for realizing highly tunable nonreciprocal devices based on Kerr magnons.

💡 Research Summary

The authors present a hybrid cavity‑magnon platform designed to achieve highly tunable nonreciprocal bistability. The system consists of two three‑dimensional microwave cavities: a parametrically driven cavity (PDC) that incorporates a second‑order nonlinear medium, and a magnonic cavity (MC) that houses a yttrium‑iron‑garnet (YIG) sphere supporting Kerr‑type magnons. The PDC provides a parametric gain term with strength λ, while the MC couples linearly to the magnons with strength g. The two cavities are linked by a photon‑photon hopping rate J. External coherent drives Ω₁, Ω₂, and Ωₘ address the PDC, MC, and the magnons, respectively, and intrinsic losses κ₁, κ₂, and γₘ are included via quantum Langevin equations.

In the steady‑state limit the authors solve the coupled nonlinear equations and obtain an expression for the mean magnon number M = |mₛ|². M satisfies a quintic polynomial whose coefficients depend on the system parameters and on which cavity is driven. By comparing the coefficients for left‑incident (Ω₁ ≠ 0, Ω₂ = 0) and right‑incident (Ω₂ ≠ 0, Ω₁ = 0) excitations, they derive an “impedance‑matching” condition: c₂