Model-based spectral inference in noisy physical time series: applications in laser linewidth estimation and precision magnetometry

This dissertation introduces and applies model-based inference techniques for spectral analysis of noisy physical time series. Two distinct experimental settings – narrow-linewidth semiconductor lasers and spin-precession-based magnetometry – pose inverse problems that traditional methods struggle with due to low signal-to- noise ratios, nonstationary dynamics, and convolutional measurement effects. Spectral estimation is crucial in precision metrology, laser diagnostics, and fun- damental physics experiments. Often, the signal of interest isn’t directly observed but inferred through a noisy, nonlinear measurement process. Challenges arise from ill-posed inversion problems, temporally correlated noise, and limited statistical res- olution, particularly in low-SNR regimes. Standard approaches frequently overlook physical structure and fail to propagate uncertainty properly, motivating inference methods that integrate domain-specific knowledge, parametric signal models, and well-defined statistical behavior under experimental constraints. Three studies form this work’s core. The first presents a parametric Wiener filter- ing framework using a power spectrum equalization (PSE) criterion to deconvolve laser frequency noise spectra from delayed self-heterodyne (DSH) measurements, addressing spectral nulls and measurement noise. The second applies Bayesian in- ference to the laser system, deriving a likelihood function for the observed spectrum and estimating FN-PSD parameters via Markov Chain Monte Carlo. The third focuses on frequency tracking in free spin precession (FSP) signals from 3He mag- netometry, employing an extended Kalman smoothing approach with Expectation – Maximization-based automatic tuning of model parameters. These methods illustrate how incorporating physical system knowledge into sta- tistical inference enhances the accuracy and robustness of spectral estimation in low-SNR and dynamically filtered regimes. Validation includes synthetic and ex- perimental datasets, emphasizing reproducibility, uncertainty quantification, and computational efficiency. The techniques extend beyond the two systems studied.