This thesis presents PhD work at the Institute for Gravitational Research and Caltech LIGO Lab that was done between October 2021 and February 2026 as part of the PhD programme. The overarching aim is to develop and validate key experimental technologies that enable precision displacement measurements at the levels required for gravitational-wave detectors and their future upgrades, with a particular focus on cryogenic instrumentation, low-noise sensing, and optical readout. The work spans two closely connected contexts: (i) the Glasgow Cryogenic Interferometer Facility (GCIF), a cryogenic GW detector prototype facility intended to directly measure coating thermal noise by monitoring the thermal noise in a short Fabry–Pérot cavity; and (ii) Advanced LIGO upgrade activities at the Caltech LIGO Laboratory, centred on the Output Mode Cleaner (OMC) and readout architectures relevant to squeezed-light operation and balanced homodyne detection. A major component of this thesis addresses the suspension design required to realise a cryogenic coating-thermal-noise measurement in GCIF. Achieving the target sensitivity demands simultaneous control of multiple competing requirements: strong isolation from ground and platform motion at frequencies of interest, practical integration into a compact cryostat, and compatibility with cryogenic heat-load constraints. To meet these goals, a common platform suspension architecture is developed and analysed, in which the two suspension chains that form the cavity share a common top stage to enhance practical implementability and enable partial common-mode rejection. A combination of analytical modelling, numerical eigenmode studies, and state-space simulations is used to quantify longitudinal isolation, cross-coupling between degrees of freedom, and mode visibility across the chain. These studies inform design choices such as mass distribution, wire parameters, and damping strategy. The outcome is a mechanically feasible suspension concept with a clear pathway to prototyping and commissioning, together with a modelling workflow that connects design parameters to measurable performance metrics and supports iterative refinement. To control and read out the motion of cryogenic suspended stages, the thesis discusses development of a low-noise cryogenic shadow sensor, designed to provide robust local displacement sensing with minimal heat load. The sensor concept employs an infrared LED source, a flag attached to the moving stage, and an InGaAs quadrant photodiode (QPD) readout. The work presents a systematic experimental characterisation of LED and photodiode performance at cryogenic temperature, including optical efficiency, relative intensity noise, and electronic noise contributions. Particular emphasis is placed on identifying practical operating points that maximise displacement sensitivity and dynamic range while maintaining cryogenic compatibility. The sensor geometry is explored to understand how beam size, flag dimensions, and alignment tolerances shape linearity and noise performance, and how these trade-offs propagate into suspension damping capability. The resulting sensor design and measurement results establish a quantitative basis for sensor selection and integration in GCIF, and more broadly demonstrate an approach to engineering cryogenic-compatible displacement sensors where thermal budget and low-frequency stability are both critical. We achieved a shot-noise-limited displacement sensitivity of ∼ 5×10−10m/√Hz for f ≳ 100Hz. We also discuss how this can be improved further. The thesis also reports work at the Caltech LIGO Laboratory (January–October 2023, April–July 2024, and August 2025) related to optical filtering and readout in kilometre-scale detectors. A central component is the Output Mode Cleaner (OMC), which rejects higher-order spatial modes and radio-frequency sidebands at the interferometer output, thereby reducing technical noise couplings and improving the effectiveness of squeezed-light operation. This work contributes to the development and characterisation of enhanced OMCs that meet the high-throughput requirements of greater than 98% efficiency for the next upgrade of LIGO. These upgrades are closely linked to the adoption of balanced homodyne detection (BHD) in the O5 era: an enhanced readout scheme that enables full use of squeezed light and reduces quantum noise by reading out the interferometer signal via interference with a local oscillator. In this context, the thesis highlights key practical complexities associated with deploying BHD on a kilometre-scale detector, and assesses the feasibility of a polarisation-based implementation as an alternative strategy. The final chapter develops the mathematical framework and modelling tools required to analyse polarisation BHD, and presents an experimental demonstration that validates the approach and informs requirements for robust, high-efficiency readout.
Thejas Seetharamu (Thu,) studied this question.