Quantum Metrology for Enhanced Gravitational-Wave Detection

Current ground-based gravitational wave detectors are reaching sensitivity limits imposed by quantum, thermal, seismic, and Newtonian noise, motivating the development of novel techniques to surpass these fundamental barriers. This thesis investigates two complementary approaches to enhance interferometric gravitational wave astronomy: displacement-noise-free interferometry (DFI) and real-time waveform estimation via Kalman filtering. First, we introduce a resonant triangular-cavity topology that, by exploiting redundant readout channels, isolates phase shifts induced by gravitational waves from mirror displacement noise. Within an input–output formalism, we define the displacement-free subspace as the null space of the mirror-noise transfer matrix and demonstrate that this configuration retains finite quantum Fisher information even in the limit of arbitrarily large mirror motion. Incorporating realistic thermal and radiation-pressure noise models, we derive optimal homodyne detection angles, characterize pseudo-displacement-free modes over finite bandwidths, and quantify the effect of injected squeezing. Extensions to n-gon cavity networks further establish the versatility and practical feasibility of the DFI paradigm. Second, we cast the readout of detuned interferometers as a multi-parameter estimation problem, where gravitational-wave signals couple amplitude and phase quadratures. To recover the quantum Cramér–Rao bound for a chosen quadrature, we design Bayesian filters --- specifically, Extended and Unscented Kalman Filters --- that treat the orthogonal quadrature as an effective disturbance. Numerical simulations under realistic signal-to-noise conditions reveal that these filters attain the optimal bound for amplitude estimation while providing reliable uncertainty quantification, matching the performance of particle-filter approaches at a fraction of the computational cost. By combining architectural immunity to displacement noise with algorithmic optimality in waveform extraction, this work lays a foundation for quantum-enhanced, broadband gravitational wave observatories. The results inform near-term upgrades and guide the conceptual design of third-generation detectors (e.g., Einstein Telescope, Cosmic Explorer), where mitigating low-frequency environmental noise and delivering real-time signal processing are critical.