Arm Locking Using a Transfer Oscillator

Space-borne gravitational wave (GW) detectors are able to open the low-frequency window from 0.1 mHz to 1 Hz, which the ground-based GW detectors can not access. Arm locking is a technique, with which the laser frequency can be stabilized to the intersatellite arm length, to further reduce the risk of time delay interferometry (TDI). Clock noise is one of the main sources limiting the ultimate performance of arm locking. In this work, we experimentally demonstrate arm locking with a transfer oscillator, by using an electrical delay unit. We develop a low-noise transfer oscillator based on the laser frequency comb, which can coherently generate a clock signal traceable to the stabilized laser. The transfer noise can achieve $4.2\times 10~^{{-8}}$ Hz/Hz $^{{1/2}}$ at 0.7 mHz, and $2.7\times 10~^{ {-7}}$ Hz/Hz $^{ {1/2}}$ at 0.1 Hz. We examine the performances of single-arm locking and modification of dual-arm locking. The experimental results show that, with the help of the transfer oscillator, the noise performance of arm locking can be improved, since the clock noise has been removed. Moreover, we carry out TDI after the implementation of arm locking, and the noise performance can well meet the requirement of GW detection. Our work could provide a valuable method for the frequency-comb based arm locking and TDI in the future space-borne GW detections.