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.
U. D. Jentschura, "Separation of Transitions with Two Quantum Jumps from Cascades," Physical Review A - Atomic, Molecular, and Optical Physics, vol. 81, no. 1, pp. 012112-1-012112-8, American Physical Society (APS), Jan 2010.
The definitive version is available at http://dx.doi.org/10.1103/PhysRevA.81.012112
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)
Article - Journal
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