发表机构
Faculty of Physics, University of Tabriz; Department of Physics, Kocaeli University（大不里士大学物理学院; 科贾埃利大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出SQUID端接超导腔作为窄带参数换能器探测高频引力波，通过推导模谱和响应核函数，区分共振频率与光子对产生响应，并建立Mathieu型参数放大理论，为窄带换能提供框架。
AI 中文摘要
兆赫至吉赫兹范围内的高频引力波需要超越传统干涉仪的探测策略。我们研究了一种SQUID端接的超导微波腔作为窄带参数换能器的响应。利用腔边界条件和约瑟夫森电感的磁通依赖性，推导了四分之一波模谱以及物理线长、相速度和SQUID电感长度变化时的一阶本征频率响应。通过将微扰动力学投影到静态腔模上，我们证明了共振频率响应与光子对产生响应通常是不同的。因此，我们引入了两个独立的核函数，$R_n^{\omega}$ 和 $R_n^{\rm pair}$，它们仅在模式归一化和空间分布的变化可以忽略时才重合。在 $\Omega_{\rm GW}\simeq 2\omega_n$ 附近，孤立模动力学简化为Mathieu型参数放大器，从而可以在存在耗散的情况下获得光子数、正交方差、增益和不稳定性阈值。自发光子产生随引力波应变呈二次方缩放，对于代表性参数而言极其微小，而带有相干探针的相位敏感响应可以随应变呈线性缩放。因此，该框架为窄带引力波换能提供了理论描述，而定量灵敏度估计则需要针对具体器件校准机械-电磁响应、验证模式隔离性，并对损耗和噪声进行完整处理。
英文摘要
High-frequency gravitational waves in the MHz--GHz range require detection strategies beyond conventional interferometers. We study the response of a SQUID-terminated superconducting microwave cavity as a narrowband parametric transducer. The cavity boundary conditions and the flux dependence of the Josephson inductance are used to derive the quarter-wave mode spectrum and the first-order eigenfrequency response to changes in the physical line length, phase velocity, and SQUID inductive length. By projecting the perturbed dynamics onto the static cavity modes, we show that the resonance-frequency response and the photon-pair-production response are generally distinct. We therefore introduce two independent kernels, $R_n^ω$ and $R_n^{\rm pair}$, which coincide only when changes in mode normalization and spatial profiles can be neglected. Near $Ω_{\rm GW}\simeq 2ω_n$, the isolated-mode dynamics reduce to a Mathieu-type parametric amplifier, allowing the photon number, quadrature variances, gain, and instability threshold to be obtained in the presence of dissipation. Spontaneous photon production scales quadratically with the gravitational-wave strain and is extremely small for representative parameters, whereas phase-sensitive responses with a coherent probe can scale linearly with strain. The framework therefore provides a theoretical description of narrowband gravitational-wave transduction, while a quantitative sensitivity estimate requires device-specific calibration of the mechanical--electromagnetic response, verification of mode isolation, and a complete treatment of loss and noise.
