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.
Description:
This thesis investigates the fundamental limits of laser coherence and linewidth from the perspective of quantum optics and quantum metrology. The work begins with an introduction to the quantization of the electromagnetic field, coherent states, phase operators, and open quantum system dynamics using Lindblad and Langevin formalisms. Building on these foundations, the thesis develops the theory of laser coherence and phase diffusion in quantum optical systems.
The study further explores concepts from classical and quantum estimation theory, particularly Fisher Information and precision bounds, to analyze laser phase estimation and coherence properties. Special emphasis is placed on understanding the Heisenberg limit in laser systems and the role of resource constraints in achieving enhanced phase stability. Models of gain saturation, phase diffusion, and Heisenberg-limited laser behavior are examined in detail, with discussion on the Hamiltonian structure and resource accounting necessary for realizing such limits.
Overall, the thesis connects laser linewidth reduction with principles of quantum parameter estimation and provides a resource-based perspective on achieving Heisenberg-limited coherence in laser systems.
