TRANSITION OPERATORS IN RADIATIVE DAMPING THEORY

The application of transition operators Pm,m′(t)=exp(iHt)|mm′|exp(-iHt) is studied for the problem of an atomic system S with eigenstates {m} interacting with one or more damping reservoirs R. The average value of these operators gives the reduced density matrix ρm′,m(S)(t) for S. If R consists of broad-band distributions of harmonic oscillators, (e.g., radiative damping), then damped equations of motion can be derived for all Pm,m′(t), even if S is a multilevel system. One need not specify the initial states of R, nor restrict the treatment to second order in the S-R coupling. The formalism is illustrated for the case where S consists of (i) a four-level atom in a resonant cavity (with broad-band modes also present), and (ii) a collection of atoms that can be treated as a multilevel spin system. Density-matrix equations are obtained for the case where no damping radiation is present initially. In (ii), the formalism is used to derive a two-time corrleation function without the aid of the fluctuation-regression theorem. © 1969 The American Physical Society.