CHAPTER 5 The Decay of Coupled States

Victor M. Galitski, Boris Mikhailovich Karnakov, Vladimir I Kogan +1 more

Abstract This chapter analyzes problems on spin s = ½; spin-orbital states with spin s = ½ (higher spins); spin density matrix (angular distributions in decays); bound states of spin-orbit-coupled particles; and coherent-state spin path-integral.

Marlan O. Scully, Muhammad Suhail Zubairy

In many problems in quantum optics, damping plays an important role. These include, for example, the decay of an atom in an excited state to a lower state and the decay of the radiation field inside a cavity with partially transparent mirrors. In general, damping of a system is described by its interaction with a reservoir with a large number of degrees of freedom. We are interested, however, in the evolution of the variables associated with the system only. This requires us to obtain the equations of motion for the system of interest only after tracing over the reservoir variables. There are several different approaches to deal with this problem. In this chapter, we present a theory of damping based on the density operator in which the reservoir variables are eliminated by using the reduced density operator for the system in the Schrödinger (or interaction) picture. We also present a ‘quantum jump’ approach to damping. In the next chapter, the damping of the system will be considered using the noise operator method in the Heisenberg picture. An insight into the damping mechanism is obtained by considering the decay of an atom in an excited state inside a cavity. The atom may be considered as a single system coupled to the radiation field inside the cavity. Even in the absence of photons in the cavity, there are quantum fluctuations associated with the vacuum state. As discussed in Chapter 1, the field may be visualized as a large number of harmonic oscillators, one for each mode of the cavity.

Gastón García‐Calderón

Pavel Exner

P. L. Knight, B. M. Garraway

This chapter describes how the nonclassical states are peculiarly sensitive to dissipation when the coupling of the field modes to their larger environment is taken into account. Well before the field energy is significantly dissipated, the coherences responsible for the nonclassical behaviour will decay, at a ‘decoherence rate’ determined by the square of the separation of the constituent components of the nonclassical superpositions in phase-space. The Wigner functions for each Fock state component are given by Laguerre polynomials. These interfere to generate the superposition of interest. Coherences are destroyed at a rate which is proportional to the degree of excitation of the system as the system relaxes to a statistical mixture of relevant ‘pointer bases’. The chapter shows how the dissipative environment ‘deconstructs’ the field into its appropriate constituent parts. The chapter examines the Jaynes-Cummings system governed by the Milburn equation and shows how the intrinsic decoherence modifies the time evolution of the atomic inversion.