Arm locking using laser frequency comb

Abstract

The space-borne gravitational wave (GW) detectors, e.g., LISA, TaiJi, and TianQin, will open the window in the low-frequency regime (0.1 mHz to 1 Hz) to study the highly energetic cosmic events, such as coalescences and mergers of binary black holes and neutron stars. For the sake of successful observatory of GWs, the required strain sensitivity of the detector is approximately 10−21/Hz1/2 in the science band, 7 orders of magnitude better than the state of the art of the ultra-stable laser. Arm locking is therefore proposed to reduce the laser phase noise by a few orders of magnitude to relax the burden of time delay interferometry. During the past two decades, various schemes have been demonstrated by using single or dual arms between the spacecraft, with consideration of the gain, the nulls in the science band, and the frequency pulling characteristics, etc. In this work, we describe an updated version of single arm locking, and the noise amplification due to the nulls can be flexibly restricted with the help of optical frequency comb. We show that the laser phase noise can be divided by a specific factor with optical frequency comb as the bridge. The analytical results indicate that, the peaks in the science band have been greatly reduced. The performance of the noise suppression shows that the total noise after arm locking can well satisfy the requirement of time delay interferometry, even with the free-running laser source. When the laser source is pre-stabilized to a Fabry-Perot cavity or a Mach-Zehnder interferometer, the noise can reach the floor determined by the clock noise, the spacecraft motion, and the shot noise. We also estimate the frequency pulling characteristics of the updated single arm locking, and the results suggest that the pulling rate can be tolerated, without the risk of mode hopping. Arm locking will be a valuable solution for the noise reduction in the space-borne GW detectors. We demonstrate that, with the precise control of the returned laser phase noise, the noise amplification in the science band can be efficiently suppressed based on the updated single arm locking. Not only does our method allow the suppression of the peaks, the high gain, and low pulling rate, it can also serve for full year, without the potential risk of locking failure due to the arm length mismatch. We then discuss the unified demonstration of the updated single arm locking, where both the local and the returned laser phase noises can be tuned to generate the expected arm-locking sensor actually. Finally, the time-series simulations in Simulink have been carried out, and the results indicate a good agreement with the theory, showing that the presented method is reasonable and feasible. Our work could provide a back-up strategy for the arm locking in the future space-borne GW detectors.