Suppression of clock-jitter noise and laser phase noise in arm locking

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.