Arm locking in conjunction with time-delay interferometry

Abstract

A crucial challenge to the ongoing endeavor of spaceborne gravitational wave (GW) detection resides in the laser phase noise, typically 7 to 8 orders of magnitude above the inevitable noise. The arm-locking technique was proposed to suppress the noise in prestabilized laser beams. Based on the feedback control theory, it is implemented by appropriate design of the signal routing architecture, particularly the controllers' transfer functions. Theoretically and experimentally, the technique has been demonstrated to be capable of suppressing the laser phase noise by approximately 2-4 orders of magnitude while taking into account various aspects, such as the gain and distribution of nulls in the Bode plot and the laser frequency pulling associated with the Doppler frequency subtraction. Consequently, the resultant noise floor is composed of the sources attributed to the clock jitter, optical bench motion, test mass fluctuations, and shot-noise phase fluctuations at the photodetectors, whereas the magnitudes of these noises largely remain unchanged during the process. In addition, the original GW signals are deformed through the arm-locking control loop and therefore bear specific features governed by the associated arm-locking scheme. Nonetheless, the remaining laser phase noise from the arm-locking feedback routing settles within the capability threshold of the time-delay interferometry (TDI). In this regard, it is generally understood that the output of arm locking furnishes the input of TDI, through which the residual noise is further reduced to the desired level at a postprocessing stage. In this work, we investigate the specific schemes regarding how the arm-locking output is processed further by the TDI algorithm. Specific forms of the TDI combinations are derived in accordance with suppressed laser phase noise and deformed signals of GWs. To the best of our knowledge, such explicit TDI schemes aiming at the processed signals by the arm-locking technique have not been explored in the literature. Also, we propose a real-time acousto-optic modulation scheme to compensate for the noise due to optical bench motion. The resultant noise floor, in turn, is primarily composed of those due to the test mass noise and shot noise. The sensitivity curves are evaluated and indicate that the resulting performance meets the requirement of the Laser Interferometer Space Antenna detector. Although the forms of the obtained arm-locking TDI solutions are different from the conventional ones, the response functions, residual noise power spectral densities, and sensitivity curves are found to be identical to their counterparts. Further implications of the present findings are also addressed.