Minimizing Laser Linewidth under Finite Resource Constraints: A Quantum Metrology Approach

Abstract

The coherence of laser light is a fundamental property that plays a crucial role in precision measurements, interferometry, and quantum technologies. Understanding the physical mechanisms that determine laser linewidth and phase stability is therefore an important problem in quantum optics. In this thesis, we study how laser systems can be modeled and how their coherence properties can be analyzed within a quantum mechanical framework. We first review the basic principles of quantum optics and laser theory, focusing on the description of phase diffusion that leads to the finite linewidth of a laser. We then introduce the tools of estimation theory and use them to analyze the phase diffusion process in terms of Fisher Information and estimation precision. This perspective allows us to connect the coherence properties of lasers with fundamental limits on parameter estimation. In particular, we discuss the emergence of Heisenberg-limited scaling in models of laser coherence and examine the conditions required to achieve such limits. Finally, we analyze these limits from a resource-accounting perspective, highlighting how the structure of the Hamiltonian and the available physical resources constrain the realization of Heisenberg-limited lasers.