title: Dual-reference laser stabilization for LISA using interferometer arms and optical cavity.
Creators: name: Valliyakalayil, Jobin
Publisher: name: The Australian National University
Year: 2025

description: The thesis proposes a new laser stabilization for the LISA mission that can be deployable at any point during its lifetime. The scheme is analytically computed using numerical simulations and tested in a scaled-down bench-top experiment to emphasise the feasibility of the solution. Laser Interferometer Space Antenna (LISA) is a space-borner gravitational wave (GW) detector that aims to detect GW in the low-frequency band of 0.1 mHz to 1 Hz. Proposed to be launched in 2035, LISA will consist of three spacecraft separated by 2.5 million km that orbit the Sun. GW is detected by tracking spacecraft separations using laser interferometry in which laser frequency noise is a technical challenge that impedes accurate displacement measurements. As part of its baseline, LISA employs Pound-Drever-Hall (PDH) locking scheme to lock to a cavity and perform Time-Delay-Interferometry(TDI) as a post-processing step to reduce the laser noise further. Arm locking is an alternate laser stabilization for LISA, adapted from ground detectors, wherein the laser is stabilized to the arms of the interferometer or the spacecraft separation in the case of LISA. The arms provide the best stability possible for the laser and can provide margins for TDI suppression requirements. This technique has been studied over 2 decades, in which a viable controller scheme and noise performance are outlined. Another metric that is analyzed is Doppler pulling, a fundamental limit for arm locking in LISA. Doppler pulling is the drift of laser frequency due to the orbital motion of the spacecraft affecting the feedback loop of arm locking. The Doppler pulling is shown to be reducible with appropriate sensor design and knowledge of the orbits. However, the integration of arm locking with other stabilization requires changes to the optical architecture for LISA. In this thesis, we introduce a new stabilization technique that combines both arm-locking and cavity stabilization by locking the laser to both references simultaneously. The scheme aims to require no (or minimal) changes on the baseline optical hardware, relying only on the ability to upload bitstreams to the digital platform and acquire precise information on the arm-length changes. The digital controller is outlined here along with the overall transfer function and the suppression function of one sensor on the other. A noise budget is plotted with the noise sources described in previous literature on LISA, with the combined system improving the TDI margin by at most 3 orders to the point first-generation TDI would suffice. The Doppler pulling is also simulated and shown to be within the cavity linewidth with precise Doppler knowledge. A Simulink model is designed to observe the combination in the time domain and verify the analytical models. A demonstration is also done using an experimental setup to test the viability of the combined arm-cavity system. A laser operating at 1064nm is locked to an optical cavity, with similar specifications proposed for LISA, and a Mach-Zehnder interferometer using 10 km optical fiber. By carefully designing the digital controller implemented on a commercial Field Programmable Gate Array (FPGA), we achieved a laser lock to both references for more than 15 hours at 150 kHz bandwidth. The system encompasses 7 nulls of the arm sensor by utilizing three actuators to control the laser. The results from the experiment address the key characteristics of the controller such as stability, suppression transfer functions and digital implementation of the filters. The residual noise of the system is measured by individually locking the laser to each sensor and in combination. Doppler pulling is also simulated in the experiment, and shown to be suppressed by the cavity sensor, with the performance dictated by the controller design. By comparing the experimental results to analytical models, we verified the combined arm-cavity locking and showed the viability of the controller.