Ground-based interferometers must aggressively filter noise while preserving their fundamental signal response. In the Laser Interferometer Gravitational-Wave Observatory (LIGO), this requires active alignment control that rejects low-frequency noise without reducing astrophysical sensitivity; in Gravity from the Quantum Entanglement of Space Time (GQuEST), the challenge is optical, requiring filter cavities to strip laser noise and carrier light before photon counting.
\r\n\r\nTo improve LIGO alignment control, this thesis develops an optimal-control framework that balances residual angular motion against control noise coupled into the gravitational-wave readout. A generalized state-space model represents both effects and converts the strain-coupled noise into binary-neutron-star detection-range loss. An H∞-bounded H2 synthesis minimizes the combined cost while enforcing robustness. Sweeping the performance weights and robustness bound produces a Pareto front among detection range, angular motion, and stability. Applied to a Hanford arm-cavity yaw loop, the method reduces modeled range loss by roughly an order of magnitude and angular root-mean-square motion by up to a factor of four relative to the current controller at comparable robustness.
\r\n\r\nFinite-precision arithmetic introduces rounding noise into digital feedback filters, and mathematically equivalent realizations can differ by orders of magnitude. The state-space conditioning used to make the high-dynamic-range H2/H∞ synthesis numerically tractable can also reduce rounding noise in filter realizations. A proof-of-concept scan of Caltech 40 m filters finds that LIGO's Low-Noise Biquad Form I gives the lowest noise most often, while conditioned state-space forms perform better for many individual filters.
\r\n\r\nA new experiment, GQuEST, is a tabletop interferometer designed to search for quantum-spacetime fluctuations with a photon-counting readout. Laser phase-noise sidebands in the counting band would be indistinguishable from signal photons. This thesis details how the laser filter cavity (LFC) was designed, built, commissioned, and operated to suppress these sidebands before the interferometers while transmitting the carrier. Fast laser-frequency and slow cavity-length feedback keep the carrier resonant so the passive cavity response rejects the phase-noise sidebands. Vacuum commissioning demonstrates sub-nanometer length motion; ringdowns give finesse near 4000, corresponding to about 60 dB of suppression at the readout offset.
\r\n\r\nAfter the interferometers, the photon-counting readout presents the complementary problem: the selected signal sideband must be isolated from residual carrier light and extraneous classical noise. The output-filter design uses a four-cavity output filter cavity (OFC) chain to transmit this sideband while rejecting the carrier. Frequency-shifted second-harmonic fields provide auxiliary locks for the individual cavities, and their lengths are staggered so unwanted longitudinal and higher-order-mode resonances do not overlap across the chain. OFC 1 was built and commissioned, with ringdowns giving finesse near 3500. Its measured root-mean-square residual motion lies just within the alignment scale required to retain 90% of the signal power through the four-cavity passband. Modeling of the full chain predicts carrier rejection above 200 dB while preserving signal-sideband transmission.
", "doi": "10.7907/bpa3-6410", "publication_date": "2027", "thesis_type": "phd", "thesis_year": "2027" } ]