The Laser Interferometer Space Antenna (LISA) will be the first dedicated space based gravitational wave detector. LISA will consist of a triangular formation of spacecraft, forming an interferometer with $5\times {10}^6\mathrm{km}$ long arms. Annual length variations of the interferometer arms prevent exact laser frequency noise cancellation. Despite prestabilization to an optical cavity the expected frequency noise is many orders of magnitude larger than the required levels. Arm locking is a feedback control method that will further stabilize the laser frequency by referencing it to the $5\times {10}^6\mathrm{km}$ arms. Although the original arm locking scheme produced a substantial noise reduction, the technique suffered from slowly decaying start-up transients and excess noise at harmonic frequencies of the inverse round-trip time. Dual arm locking, presented here, improves on the original scheme by combining information from two interferometer arms for feedback control. Compared to conventional arm locking, dual arm locking exhibits significantly reduced start-up transients, no noise amplification at frequencies within the LISA signal band, and more than 50 fold improvement in noise suppression at low frequencies. In this article we present a detailed analysis of the dual arm locking control system and present simulation results showing a noise reduction of 10 000 at a frequency of 10 mHz.

• Received 2 June 2008

DOI:https://doi.org/10.1103/PhysRevD.78.082001