Spectral-Temporal Structure in Quantum Light for State Reconstruction and Metrology

This thesis explores how spectral-temporal structure in quantum optical fields can be used for state reconstruction and metrology. We utilize continuous-frequency modes as a framework for describing quantum correlations and parameter encoding. In the first part, we develop compressive stimulated emission tomography (CSET) to reconstruct the joint spectral amplitude (JSA) of biphoton states generated through spontaneous parametric downconversion. We perform stimulated emission measurements together with compressive sensing methods to recover high-dimensional quantum states from a reduced dataset. Spectral phase is incorporated using frequency-resolved optical gating, which experimentally characterizes the spectral amplitude and phase of the seed pulses and allows them to be directly integrated into the reconstruction model. The resulting inverse problem is formulated as a constrained convex optimization task, enabling recovery of the full complex JSA. Informational completeness certification is used to evaluate the adequacy of the measurement set, and the method is validated using both simulated and experimental data, showing accurate and robust reconstruction under noise and limited sampling. In the second part, we study quantum metrology in structured optical fields, focusing on frequency-comb ranging in dispersive media. We use quantum Fisher information to relate parameter sensitivity to spectral mode geometry. Our results suggest that bandwidth and modal structure play a significant role in determining precision, while squeezing offers limited benefit under loss. Overall, spectral-temporal modes appear to play a central role in both quantum state reconstruction and metrology tasks considered in this work.