Quantum Laser Theory: Master Equation Approach

Miguel Orszag

Miguel Orszag

Franco Fagnola, Carlos M. Mora

Heinz‐Peter Breuer, Francesco Petruccione

Abstract This chapter introduces the fundamentals of the description of the quantum dynamics of open systems in terms of quantum master equations, together with its most important applications. Special emphasis is laid on the theory of completely positive quantum dynamical semigroups, which leads to the concept of a quantum Markov process. It discusses the relaxation to equilibrium and the multi-time structure of quantum Markov processes, as well as their irreversible nature which is characterized by an appropriate entropy functional. Microscopic derivations for various quantum master equations are presented, such as the quantum optical master equation and the master equation for quantum Brownian motion. As a further application, the master equation describing continuous measurements is derived and used to study the quantum Zeno effect. The chapter also contains a treatment of non-linear, mean field quantum master equations together with applications to laser theory and super-radiance.

Kazuro Kikuchi

This study summarizes the theory of laser-amplifier noise based on the master equation, the quantum-mechanical Langevin equation, and the rate equation. The three approaches are used differently depending on the application. Laser-amplifier noise in the direct-detection receiver is described by the master equation. Meanwhile, the quantum-mechanical Langevin equation is most effective for analyzing noise appearing in coherent optical communication systems. The rate equation approach provides a clear understanding of the intensity-noise characteristics of laser oscillators, including the amplitude squeezing.