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 | m 〉, 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 〉 → | m 〉 → | 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.



Keywords and Phrases

Atomic Transition; Cascade Process; Decay Rate; Excited Levels; General Expression; Initial State; Nonresonant; Quantum Decay; Quantum Jumps; Quantum System; Quantum Transitions; Resonance Energies; Resonance Poles; Resonant Levels; Second Orders; Time-dependent Perturbation Theory; Two Channel; Two-photon Transitions; Virtual State; Perturbation Techniques; Quantum Electronics; Quantum Interference Devices; Quantum Optics

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2010 American Physical Society (APS), All rights reserved.

Included in

Physics Commons