臂锁定中的实时多普勒频率测量与频率牵引抑制

中文摘要 AI 辅助

臂锁定是抑制天基引力波探测中激光频率噪声的一项重要技术。然而，更强的噪声抑制不可避免地会增加频率牵引的幅度，从而延长锁获取时间并增加系统不稳定的风险。为解决这一问题，本文提出了一种基于线性二次高斯控制器的实时多普勒频率测量与频率牵引抑制方法。为了在噪声抑制与牵引抑制之间取得平衡，采用了时变控制策略。在时变控制过程的初始阶段，主要目标是快速限制频率牵引。随后，牵引抑制水平逐渐放宽，同时激光频率噪声抑制能力逐步增强，使得在过渡期结束时残余频率噪声满足时延干涉测量（TDI）要求。针对多种臂锁定配置进行了全面的性能仿真。结果表明，所提出的抑制器能在约1000秒内降低频率牵引，并将其幅度限制在100 MHz以下，从而无需传统的多普勒频率预估计阶段。当使用法布里-珀罗激光器时，闭环激光频率噪声的幅度谱密度（ASD）在闭环运行2000秒和9200秒后分别满足第二代和第一代TDI的要求。这些结果表明，所提出的抑制器既能提供快速的频率牵引抑制，又能实现高水平的激光频率噪声抑制。这种新方法为臂锁定的快速获取和锁定提供了一条可行途径。

英文摘要

Arm-locking is an important technique for suppressing laser frequency noise in space-based gravitational-wave detection. However, stronger noise suppression inevitably increases the magnitude of frequency pulling, thereby prolonging the lock-acquisition time and increasing the risk of system instability. To address this issue, this paper proposes a real-time Doppler-frequency measurement and frequency-pulling suppression method based on a linear-quadratic-gaussian controller. To achieve a balance between noise suppression and pulling suppression, a time-varying control strategy is adopted. At the initial stage of the time-varying control process, the primary objective is to rapidly limit frequency pulling. Subsequently, the level of pulling suppression is gradually relaxed while the capability for laser frequency-noise suppression is progressively enhanced, so that the residual frequency noise satisfies the time-delay interferometry (TDI) requirement by the end of the transition. Comprehensive performance simulations are conducted for several arm-locking configurations. The results show that the proposed suppressor can reduce frequency pulling within approximately 1000 s while limiting its magnitude to below 100 MHz, thereby eliminating the need for the conventional Doppler frequency pre-estimation stage. When a Fabry-Perot laser is used, the amplitude spectral density (ASD) of the closed-loop laser frequency noise meets the requirements of second-generation and first-generation TDI after 2000 s and 9200 s of closed-loop operation, respectively. These results demonstrate that the proposed suppressor provides both rapid frequency-pulling suppression and a high level of laser frequency-noise suppression. This new method provide a feasible way for rapid acquisition and locking of arm-locking.

发表机构

• School of Mechanical Engineering and Electronic Information, China University of Geosciences（中国地质大学机械与电子信息学院）
• National Gravitation Laboratory, MOE Key Laboratory of Fundamental Physical Quantities Measurement, and School of Physics, Huazhong University of Science and Technology（华中科技大学引力实验室、教育部基孔物理量测量重点实验室和物理学院）

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