空间引力波探测器中锁相配置的时钟噪声传播与标定

中文摘要 AI 辅助

在空间引力波探测器中，激光锁相将微弱接收光的相位传递给本地激光器，并将星间外差频率维持在相位计带宽内。星载超稳振荡器的波动会将这些外差相位测量引入时钟噪声，从而需要在时延干涉测量（TDI）中进行额外的标定。现有基于六个独立形成的单向测量的公式并未明确描述主从锁相配置的公共参考时钟结构。在本工作中，我们直接针对该配置构建了时钟噪声传播与标定的公式。从载波和边带读出出发，我们推导了时钟噪声耦合，并构建了一个有序的边带标定规则。该规则保留非对易时延，并适用于满足传播和时钟系数闭合条件的双分支TDI组合。对于具有相同分数频率噪声谱的相互独立的星载时钟，我们比较了有锁相和无锁相情况下的匹配实现。在采用的冻结等臂模型中，本研究所考虑的45个第二代组合（最多包含16条链路）在最终时钟标定之前，于0.1–10 mHz频带内，在锁相实现中具有更小的时钟噪声残差。对两个具有代表性的16链路组合的数值模拟重现了解析谱，并验证了所预测的降低和标定效果。这些结果表明，锁相实现降低了最终标定前的时钟噪声贡献，而主激光相位噪声的消除仍依赖于TDI。

英文摘要

In space-based gravitational-wave detectors, laser phase locking transfers the phase of weak received light to a local laser and maintains the interspacecraft heterodyne frequencies within the phasemeter bandwidth. Fluctuations of the onboard ultrastable oscillators introduce clock noise into these heterodyne phase measurements, requiring additional calibration in time-delay interferometry (TDI). Existing formulations based on six independently formed one-way measurements do not explicitly describe the common-reference clock structure of a master--slave phase-locking configuration. In this work, we formulate clock-noise propagation and calibration directly for this configuration. Starting from carrier and sideband readouts, we derive the clock-noise couplings and construct an ordered sideband-calibration rule. The rule retains noncommuting delays and applies to two-branch TDI combinations satisfying propagation and clock-coefficient closure. For mutually independent onboard clocks with identical fractional-frequency noise spectra, we compare matched realizations with and without phase locking. In the adopted frozen equal-arm model, 45 second-generation combinations with up to 16 links considered here have smaller clock-noise residuals in the phase-locking realization throughout 0.1--10~mHz, before final clock calibration. Numerical simulations of two representative 16-link combinations reproduce the analytical spectra and verify the predicted reduction and calibration. These results show that the phase-locking realizations reduce the clock-noise contribution before final calibration, while the cancellation of master-laser phase noise still relies on TDI.

发表机构

• College of Physics, Chongqing University（重庆大学物理学院）
• School of Physics and Optoelectronic Engineering, Yangtze University（长江大学物理与光电工程学院）

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