III Tools of Theoretical Quantum Optics

Abstract

This chapter discusses the tools of theoretical quantum optics. Three different theoretical techniques have been used extensively in quantum optical problems: density matrix, Green's function, and quantum noise operator techniques. However, while many workers use one or the other of these approaches, most do not include all three in their tool boxes. Therefore, the chapter provides a simple discussion of each while demonstrating some of their strengths and interconnections. This is accomplished by treating the well-known problem of a single mode of the radiation field coupled to a reservoir using the density matrix, Green's function, and quantum noise operator approaches. This helps in making simple comparisons among these theoretical approaches and to see clearly the way they provide equivalent complementary descriptions of the reservoir interaction. In addition, the chapter also explains two appendices on the density matrix and Green's function descriptions of more complicated problems.