# The performance of arm locking in LISA

## TL;DR

This paper analyzes the implementation and performance of arm locking techniques in LISA, demonstrating that it can meet frequency noise goals without pre-stabilization by optimizing sensor design and controller performance.

## Contribution

It introduces a hybrid arm locking sensor, detailed controller design, and shows arm locking alone suffices for LISA's noise reduction goals.

## Key findings

- Hybrid sensor improves noise performance and laser pulling issues.
- Arm locking achieves LISA's frequency noise target without pre-stabilization.
- Enhanced gain is possible near unity-gain frequencies, improving stability.

## Abstract

For the laser interferometer space antenna (LISA) to reach it's 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. This paper details an implementation of arm locking, studies orbital effects, the impact of errors in the Doppler knowledge, and noise limits. The noise performance of arm locking is calculated with the inclusion of the dominant expected noise sources: ultra stable oscillator (clock) noise, spacecraft motion, and shot noise. Studying these issues reveals that although dual arm locking [A. Sutton & 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 hybrid sensor, retaining the benefits of common and dual arm locking sensors. We present a detailed design of an arm locking controller and perform an analysis of the expected performance when used with and without laser pre-stabilization. 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. We show that the LISA frequency noise goal can be realized with arm locking and Time-Delay Interferometry only, without any form of pre-stabilization.