Real-Time Doppler-Frequency Measurement and Frequency-Pulling Suppression in Arm-locking

Abstract

Arm-locking is an important technique for suppressing laser frequency noise in space-based gravitational-wave detection. However, stronger noise suppression inevitably increases the magnitude of frequency pulling, thereby prolonging the lock-acquisition time and increasing the risk of system instability. To address this issue, this paper proposes a real-time Doppler-frequency measurement and frequency-pulling suppression method based on a linear-quadratic-gaussian controller. To achieve a balance between noise suppression and pulling suppression, a time-varying control strategy is adopted. At the initial stage of the time-varying control process, the primary objective is to rapidly limit frequency pulling. Subsequently, the level of pulling suppression is gradually relaxed while the capability for laser frequency-noise suppression is progressively enhanced, so that the residual frequency noise satisfies the time-delay interferometry (TDI) requirement by the end of the transition. Comprehensive performance simulations are conducted for several arm-locking configurations. The results show that the proposed suppressor can reduce frequency pulling within approximately 1000 s while limiting its magnitude to below 100 MHz, thereby eliminating the need for the conventional Doppler frequency pre-estimation stage. When a Fabry-Perot laser is used, the amplitude spectral density (ASD) of the closed-loop laser frequency noise meets the requirements of second-generation and first-generation TDI after 2000 s and 9200 s of closed-loop operation, respectively. These results demonstrate that the proposed suppressor provides both rapid frequency-pulling suppression and a high level of laser frequency-noise suppression. This new method provide a feasible way for rapid acquisition and locking of arm-locking.