We consider the general scenario of an excited level |i□ of a quantum system that can decay via two channels: (i) via a single-quantum jump to an intermediate, resonant level |m̄□, followed by a second single-quantum jump to a final level |f□, and (ii) via a two-quantum transition to a final level |f□. Cascade processes |i□→|m̄□→|f□ and two-quantum transitions |i□→|m□→|f□ compete (in the latter case, |m□ can be both a nonresonant as well as a resonant level). General expressions are derived within second-order time-dependent perturbation theory, and the cascade contribution is identified. When the one-quantum decay rates of the virtual states are included into the complex resonance energies that enter the propagator denominator, it is found that the second-order decay rate contains the one-quantum decay rate of the initial state as a lower-order term. For atomic transitions, this implies that the differential-in-energy two-photon transition rate with complex resonance energies in the propagator denominators can be used to good accuracy even in the vicinity of resonance poles.
|Journal||Physical Review A - Atomic, Molecular, and Optical Physics|
|Publication status||Published - Jan 20 2010|
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics