Multi-transparent Window Phenomenon in Coupled Cavity Magnomechanical System

Qinghong Liao; Kun Peng; Menglin Song

doi:10.3788/CJL230879

Abstract

Objective

With the rapid developments in nanotechnology, cavity optomechanics has become an important research topic in quantum mechanics. Magnomechanical cavity systems have attracted considerable attention in recent years. Compared to the cavity optomechanical system, the cavity magnomechanical system exhibits many benefits such as high spin density, high cooperativity with microwave photons, and a very low damping rate. Therefore, this study provides a new platform for examining interactions between light and matter. This study analyzes the multi-transparent window phenomenon, fast- and slow-light effects, and precision measurements in a coupled cavity magnomechanical system. These results have potential applications in quantum information processing and high-precision measurements.

Methods

In this study, we commence with a coupled cavity magnomechanical system model. The hybrid cavity magnomechanical system consists of two yttrium iron garnet (YIG) balls located near the maximum magnetic field of the two resonant cavities, and a bias magnetic field is applied to the YIG balls in the z-direction of the two resonant cavities to excite the magnon mode and realize strong coupling with the cavity field. Mutual coupling exists between the optical fields of the two resonators, and the coupling strength is related to the distance between them. A weak probe laser beam $ε_{p}$ with frequency $ω_{p}$ is applied to the optical cavity $a_{1}$ . The total Hamiltonian of the coupled cavity-magnetic field can be obtained in a frame rotating at the frequency of the driving field. Based on the Heisenberg equation and input-output relationship, we can obtain the output field ( $ε_{o u t}$ ) expression and group delay ( $τ$ ) expression of the system. Subsequently, the effects of various parameters on the optical response of the system are investigated.

Results and Discussions

When the coupling between two microwave cavities and magnon-phonon coupling are absent, there is only photon-magnon coupling between the cavity $a_{1}$ and magnon $m_{1}$ . At this time, there is a magnon-induced transparency window in the absorption spectrum generated by the interaction between the magnon and optical cavity field. We introduce various coupling terms, and the absorption spectrum of the output field exhibits different numbers of transparent windows (Fig. 2). The dispersion spectrum of the output field is plotted under the same conditions (Fig. 3). Next, the influence of the coupling strength between the two microwave cavities on the transmission characteristics of the hybrid cavity magnomechanical system is examined. These results indicate that better transparency can be realized in the output field by adjusting the coupling strength using the coupling strength (Fig. 4). The absorption peak heights and widths of the detection field absorption spectra are plotted as a function of the coupling strength (Fig. 5). The results indicate that the absorption peak height of the detection field absorption spectrum is inversely proportional to the coupling strength ( $J$ ) of the two microwave cavities, and the width is directly proportional to $J$ . Therefore, the coupling strength $J$ can be obtained by simply measuring the height and width of the absorption peak, which also indicates that the hybrid cavity magnomechanical system is an effective and accurate method for measuring the coupling strength $J$ . We also investigate the effects of $K_{1}$ , $K_{2}$ , $g_{2}$ , and $κ_{a_{2}}$ on the output field (Figs. 6 and 7). The results show that $g_{2}$ and $κ_{a_{2}}$ only cause a change in the position of the absorption peak of the absorption spectrum and do not affect the position of the transparent window. Finally, the functions of the group delay ( $τ$ ) with the normalized detection field detuning ( $δ / ω_{b}$ ) are plotted for different $J$ and $κ_{a_{2}}$ (Fig. 6). There are upward peaks (slow-light effect) and downward valleys (fast-light effect) near $δ = 0.7 ω_{b}$ and $δ = 1.3 ω_{b}$ , and the peak value of the group delay $τ$ decreases with an increase in cavity dissipation $κ_{a_{2}}$ and increases with an increase in coupling strength $J$ . Therefore, the conversion between fast- and slow-light effects can be realized by changing the dissipation and coupling strengths of the resonant cavity.

Conclusions

Based on the coupled cavity magnomechanical system, the phenomenon of multiple transparent windows and effect of slow-fast light are investigated. The output characteristics of the system are discussed using quantum optics theory and standard input-output relations. The results show that different numbers of transparent windows can be obtained by adjusting the system parameters, and better transparency can be realized. Simultaneously, a method for precisely measuring the interaction strength between the two cavities is proposed by measuring the height and width of the absorption peaks. Additionally, fast-slow light conversion can be achieved by adjusting the system parameters. This scheme has important guiding significance for research on precision measurements and quantum information processing.