A master equation approach to nonlinear optics and chemical reactions

Abstract

Part 1 of this thesis consists of a theoretical quantum statistical analysis of several nonlinear optical processes. As an introduction a master equation describing the time behaviour of the field in a general irreversible nonlinear interaction between an optical photon field and a number of two level atoms is given. This master equation is then used to calculate the exact time dependent statistical properties of the light fields in certain special processes: two photon emission by atoms, two photon absorption by atoms and Raman scattering of photons by atoms. The steady states of the emission-absorption processes are examined, and found to have interesting statistical properties not found in the field states normally met with. Part 1 is concluded with a brief examination of approximate methods of solutions for the nonlinear processes studied. Part 2 is a brief study of the nature of concentration fluctuations and correlations in chemically reacting systems, using the stochastic master equation approach. The time dependent fluctuations and spatial correlations are discussed for a space dependent model of a linear chemically reacting system. These results are compared with those obtained when correlations are ignored. The steady state behaviour of a particular nonlinear chemical system is then examined. Deterministic and non space-dependent stochastic analysis show that when certain system parameters are varied, the system’s behaviour is very similar to that of a thermodynamic system which undergoes a second order phase transition. A space-dependent analysis is then given, and this makes the analogy very close indeed.