AI 中文总结
研究高级LIGO干涉仪光轴失准的多模量子效应，建立对应信号提取腔与臂腔的耦合谐振器模型，揭示失准会降低灵敏度、重分布压缩态并产生空间模式纠缠，需将其视为多模量子过程而非简单损耗。
AI 中文摘要
我们针对高级LIGO（Advanced LIGO）干涉仪差模的简化模型，建立了光轴失准的多模量子模型。该系统被描述为对应信号提取腔和臂腔的两个耦合光学谐振器，推导了模式耦合系数的解析表达式，建立了光学元件几何扰动与多模光学动力学之间的直接联系。利用该形式体系，我们研究了光轴失准对量子噪声受限灵敏度及注入压缩态的影响。结果表明，信号提取腔与臂腔之间的失准会导致灵敏度显著下降、压缩椭圆的频率相关旋转，以及基空间模式中可观测压缩的减少；同时，注入的压缩态并未被破坏，而是在耦合空间模式间重新分布。产生的模式耦合在基模与高阶模式间生成量子关联，并通过部分转置正定准则验证了空间模式纠缠。我们的结果表明，光轴失准应被视为相干多模量子过程，而非简单的光学损耗机制。
英文摘要
We develop a multimode quantum model of optical-axis misalignment in a simplified representation of the differential mode of an Advanced LIGO interferometer. The system is described as two coupled optical resonators corresponding to the signal extraction cavity and the arm cavity. Analytical expressions for the mode-mixing coefficients are derived, establishing a direct connection between geometrical perturbations of optical elements and multimode optical dynamics. Using the developed formalism, we investigate the influence of optical-axis misalignment on quantum-noise-limited sensitivity and injected squeezed states. We show that misalignment between the signal extraction cavity and the arm cavity leads to significant sensitivity degradation, frequency-dependent rotation of the squeezing ellipse, and a reduction of the observable squeezing in the fundamental spatial mode. At the same time, the injected squeezing is not destroyed but redistributed among coupled spatial modes. The resulting mode coupling generates quantum correlations between the fundamental and higher-order modes and leads to spatial-mode entanglement verified using the positive partial transpose criterion. Our results demonstrate that optical-axis misalignment should be treated as a coherent multimode quantum process rather than as a simple optical loss mechanism.
Comments25 pages, 9 figures
