Controlling Fano resonance and slow/fast light in a magnomechanical system with an optical parametric amplifier

We study the slow-fast light effect and multi-transparency induced by magnomechanical systems. The system incorporates two magnons, which are collective magnetic excitations, placed alongside a degenerate optical parametric amplifier (OPA) within a cavity. The interaction between phonons, magnons, and light inside the cavity leads to two phenomena: magnomechanically induced transparency (MMIT) and magnon induced transparency (MIT). We show how an OPA alters the absorption and dispersion characteristics of the light spectrum. The observation of the Fano resonance through magnon-mechanical coupling with the degenerate OPA is discussed. Through tuning vibration interactions and the OPA, we achieve the improvement of slow light. We hope our findings could pave the way for advancements in quantum information processing.