As an interdisciplinary subject of nanophysics and quantum optics, the physical properties of cavity optomechanics have attracted the attention of many researchers. At the same time, with the development of optomechanical systems, cavity magnetic quantum dynamics systems have become a new platform for realizing quantum coherence and coupling between magnons, cavity photons, and mechanical oscillators. This paper proposes the simultaneous input of the control field and detection on both sides. The cavity field (one of the microcavities has a mechanical vibration mode, there is mutual coupling between the optical fields of the two resonators, and the coupling strength is related to the distance between the two resonators) and the dual-resonator magnetomechanical system are composed of magnons. On this basis, the input-output theory is used to analyze the dual-resonator magnetomechanical system under different parameter mechanisms. In the cavity output, magnons, microwave photons, and acoustics can be observed in the presence of cavity-to-cavity coupling. Various coherent properties arise from the coupling between magnons, cavity photons, and mechanical oscillators. These results are new phenomena that have not been revealed in typical electromagnetically induced transparent systems and may be applied to novel optical information-processing devices.

In this letter, we begin with a dual-cavity magneto-optical mechanical system model. We analyze the composition of the cavity and provide the definition of each parameter. The magnon directly driven by the microwave source in the cavity a can directly establish a coupling mechanism with the microwave cavity photons. A YIG ball is placed in the maximum magnetic field of the microwave resonant cavity a. In order to bias the YIG ball, a uniform external bias magnetic field needs to be applied along the z direction. The cavity mode driving magnetic field in the y direction is mainly used to deform the YIG ball. The purpose of the dynamic magnetization of the magnon is to ensure that the cavity mode driving magnetic field in the y direction and the uniform external bias magnetic field along the z direction are perpendicular to the magnetic field of the cavity mode in the x direction at the same time. The Heisenberg equation of motion, factorization, and other methods are used to solve the obtained Hamiltonian, and the relational expression between the resonator field and the output field is established. Finally, we explore the different effects under different parameters. We investigate the coherent optical response under different parameter mechanisms, such as the coupling strength (J) between the resonators and the ratio (n) of the probing light intensity of the two resonators, in the case of system interaction, and the optical response transmission characteristics of the optomechanical system can be observed.

This study shows that different properties can be observed in the cavity of a magnetomechanical system under different parameter mechanisms. In the case where the mechanical oscillator is coupled with the magnon and the probe light on the right is turned off ( ), when the coupling strength , the greater the coupling strength of the system, the more obvious the degree of transmission of the system. When the value of the coupling strength increases to , the optomechanical system exhibits complete transmission at the central resonance, and when , the system exhibits mode splitting (Fig. 2). In the case where the microwave photons are coupled with the magnons and the probe light on the right is turned off ( ), with an increase in the coupling strength between the two resonators, the peak values of the transparent peaks on both sides gradually increase, while the central resonance strength gradually decreases. When the intensities of the left and right probe light are the same ( ), the peak transmittance and reflectance of the left cavity increase with the increase of J. This is because of the quantum coherence between the left and right probe fields (Fig. 3). In the case where microwave photons, mechanical oscillators, and magnons are coupled together and the right probe light is turned off ( ), when the coupling strength between the two resonators is enhanced, the peak values of the transparent peaks on both sides gradually become larger, the peak value at the central resonance gradually becomes smaller, and the standard mode splitting phenomenon occurs. When the effective optomechanical coupling ratio is changed, the width of the transparent peak at the central resonance increases with an increase in the value; the spacing between the transparent peaks on both sides also increases. Coupling with magnons also allows a portion of the energy to be stored in the magnons (Fig. 4). When the intensity of the probe light on the left and right sides of the system is the same ( ), the transmission first increases and then decreases, and the reflection first decreases and then increases on both sides of the optical system. This phenomenon is very important (Fig. 5). Based on this phenomenon, the dynamic control of the dynamic propagation process of weak light signals can be realized, which can be used to construct photonic devices with special functions.

In this paper, based on an optomechanical system, a dual-resonator magneto-optomechanical system based on magnons is proposed. The numerical results achieved can be displayed analytically under the coupling of the magnon and mechanical oscillator, the coupling of the magnon and microwave photon, and the co-coupling of the three. The detection field is regulated by adjusting the system parameters. This dual-cavity magnetomechanical system can exhibit different optical transmission characteristics, such as mode splitting, perfect quantum expansion coherence, perfect quantum destructive coherence, and absorption of magnon energy, which are very important in the process of quantum information processing. Studying and manipulating these dynamic controls can help us understand phenomena related to cavity opto-mechanical systems from a new perspective. The proposed scheme may serve as a potential platform for realizing controllable photon transmission and developing novel photonic devices.