Displacement and inertial sensors are used to measure motion in many high-precision experiments. A prime example of such a use case is ground-based gravitational-wave detectors. To enable the detection of gravitational waves, the seismic isolation systems of these detectors employ various inertial and local displacement sensors to reduce the transmission of ground motion to the core optics of the interferometer. This thesis investigates a displacement sensing technique, named heterodyne cavity-tracking, within the context of current and future ground-based gravitational-wave detectors, as well as future lunar-based concepts. Precise length measurements with femtometer or sub-femtometer readout noise at frequencies below 10 Hz would be extremely beneficial in increasing the overall sensitivity of ground-based gravitational-wave detectors, enabling more astrophysical observations. A specific case of a lunar-based gravitational-wave detection concept involves deploying a femtometer-class inertial sensor array on the Moon's surface to identify gravitational-wave signatures. This thesis presents a heterodyne-stabilized optical cavity-based interferometer scheme that can serve as a compact, high-sensitivity displacement sensor with a fringe-scale operating range. The dynamic range for displacement readout is aimed at being increased by pushing the precision into the femtometer regime while not completely compromising the achievable operating range. Specifically, this work studies two aspects of the interferometer scheme that are crucial for achieving the desired displacement readout precision of below 1 fm/√Hz at around 1 Hz. The first aspect is the development of an ultra-fast, high-bandwidth readout system, the GHz Phasemeter, based on a field-programmable gate-array (FPGA) algorithm. The developed phasemeter is the highest bandwidth, highly stable, and fastest phase-tracking instrument reported to date. This implementation has been extended to include a Digital Heterodyne Controller (DHC), which is required for the laser-locking control loop. The second aspect involves the study of laser frequency references aimed at suppressing frequency noise in the readout. A potential frequency reference made of chalcogenide glass, which is 'athermal' in nature, has been investigated during the course of this work. Finally, these components are combined to realize a displacement sensing scheme and have been analyzed within the scope of this thesis. An overall displacement readout noise floor of less than 20 fm/√Hz has been achieved for frequencies above 5 Hz with the current experimental setup. A dynamic range of six orders of magnitude for displacement measurement has been demonstrated, reaching a maximum motion of about 0.15 µm. The work presented here was conducted between 2020 and 2024 at the Institute of Experimental Physics, University of Hamburg, Germany.
Shreevathsa Chalathadka Subrahmanya (Tue,) studied this question.