Suppression of laser phase noise by using updated common arm locking

Abstract

The space-borne gravitational wave (GW) detectors, e.g., LISA, TianQin, TaiJi, are designed to measure the GW in the low-frequency regime (0.1 mHz to 1 Hz). The arm length mismatches in the flying constellation prevent exact laser phase noise cancellation. For a typical Michelson interferometric design such as LISA, the two arms will differ by a few percent and the uncanceled fluctuation from the ultra-stable laser is about 5 orders larger than the sensitivity goal in the science band (0.1 mHz to 1 Hz). In this work, we try to resolve this discrepancy in real time by using an arm locking technique. Unlike the analysis in previous literatures, we use the subtraction of one closed loop phase meter output from another one at the main spacecraft to cancel the laser phase noise further. We find that, with a careful design of the arm locking controller, the laser phase noise can be suppressed below the level of secondary noises in most parts of the science band. We point out that since the nulls always exist in the presence the GW transfer function of Michelson interferometer, there is no need to move the nulls to outside the science band by using a complicated arm locking sensor. Then, a study on the Doppler frequency pulling for the system has been carried out, and the result suggests that the pulling rate can meet the requirement. Finally, a good agreement between the time-series simulation in Simulink and theoretical result indicates the feasibility of this scheme. Therefore, the suppression of laser phase noise can possibly be realized in real time with prestabilization and updated common arm locking techniques. Our work can provide a back-up strategy for the implementation of arm locking in future space-borne GW detectors.