Performance of arm locking in LISA

For the Laser Interferometer Space Antenna (LISA) to reach its design sensitivity, the coupling of the free-running laser frequency noise to the signal readout must be reduced by more than 14 orders of magnitude. One technique employed to reduce the laser frequency noise will be arm locking, where the laser frequency is locked to the LISA arm length. In this paper we detail an implementation of arm locking. We investigate orbital effects (changing arm lengths and Doppler frequencies), the impact of errors in the Doppler knowledge that can cause pulling of the laser frequency, and the noise limit of arm locking. Laser frequency pulling is examined in two regimes: at lock acquisition and in steady state. The noise performance of arm locking is calculated with the inclusion of the dominant expected noise sources: ultrastable oscillator (clock) noise, spacecraft motion, and shot noise. We find that clock noise and spacecraft motion limit the performance of dual arm locking in the LISA science band. Studying these issues reveals that although dual arm locking A. Sutton and D. A. Shaddock, Phys. Rev. D 78, 082001 (2008) has advantages over single (or common) arm locking in terms of allowing high gain, it has disadvantages in both laser frequency pulling and noise performance. We address this by proposing a modification to the dual arm-locking sensor, a hybrid of common and dual arm-locking sensors. This modified dual arm-locking sensor has the laser frequency pulling characteristics and low-frequency noise coupling of common arm locking, but retains the control system advantages of dual arm locking. We present a detailed design of an arm-locking controller and perform an analysis of the expected performance when used with and without laser prestabilization. We observe that the sensor phase changes beneficially near unity-gain frequencies of the arm-locking controller, allowing a factor of 10 more gain than previously believed, without degrading stability. With a time-delay error of 3 ns (equivalent of 1 m interspacecraft ranging error), time-delay interferometry (TDI) is capable of suppressing 300 Hz/Hz of laser frequency noise to the required level. We show that if no interspacecraft laser links fail, arm locking alone surpasses this noise performance for the entire mission. If one interspacecraft laser link fails, arm locking alone will achieve this performance for all but approximately 1 h per year, when the arm length mismatch of the two remaining arms passes through zero. Therefore, the LISA sensitivity can be realized with arm locking and time-delay interferometry only, without any form of prestabilization.