Arm-locking technique has been a focus of attention as one of the means to suppress the laser phase noise in space-based gravitational wave detector. The main idea of the arm-locking technique is to transfer the stability of the detector arm length to laser frequency by introducing a feedback control loop. Generally, laser phase noise will be suppressed by an amount similar to the magnitude of the controller gain. However, on the one hand, clock-jitter noise and optical bench motion noise, as the noise floor of the arm-locking technique, need to be suppressed. On the other hand, limited by the Doppler frequency pulling, the gain of the controller generally cannot be too large. It means that even if we do not consider clock-jitter noise and optical bench motion noise, it is difficult to suppress laser phase noise below the noise floor only by arm-locking technique. In this work, we combine self-referenced optical frequency combs and arm-locking technique to generate clock signals that are coherently referenced to the closed-loop laser beams, so that the clock-jitter noise is also suppressed by about the level of controller gain. We conduct a simulation on the above configuration, and the results show that the performance of the arm-locking is no longer limited by clock-jitter noise in the low-frequency band. To address the issue of insufficient laser phase noise suppression by the arm-locking technique, we further investigate time-delay interferometry (TDI) combinations under outputs of arbitrary arm-locking configurations. We obtain the equations for eliminating laser phase noise. To ensure that the TDI combinations can directly operate in the time domain, we derive a restricted solution space by assuming a specific form for the solutions.

中文翻译：

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抑制臂锁定中的时钟抖动噪声和激光相位噪声


臂锁技术作为天基引力波探测器中抑制激光相位噪声的手段之一，一直是人们关注的焦点。臂锁定技术的主要思想是通过引入反馈控制回路，将探测器臂长的稳定性转移到激光频率。通常，激光相位噪声将被抑制，其抑制量与控制器增益的大小相似。然而，一方面，时钟抖动噪声和光学工作台运动噪声作为臂锁定技术的本底噪声，需要抑制。另一方面，受多普勒频率牵引的限制，控制器的增益一般不能太大。这意味着，即使我们不考虑时钟抖动噪声和光学工作台运动噪声，仅通过臂锁定技术也很难将激光相位噪声抑制到本底噪声以下。在这项工作中，我们将自参考光频率梳和臂锁定技术相结合，以产生与闭环激光束相干相关的时钟信号，因此时钟抖动噪声也受到大约控制器增益水平的抑制。我们对上述配置进行了仿真，结果表明，在低频段，Arm-locking 的性能不再受到 clock-jitter noise 的限制。为了解决臂锁定技术对激光相位噪声抑制不足的问题，我们进一步研究了任意臂锁定配置输出下的时滞干涉 （TDI） 组合。我们得到了消除激光相位噪声的方程。为了确保 TDI 组合可以直接在时域中运行，我们通过假设解的特定形式来推导出一个受限的解空间。