Separation of Transitions with Two Quantum Jumps from Cascades

Abstract

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 |bar 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> -> |bar 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.

9 pages; RevTeX

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Cited by in corpus (5)

• Functional Form of the Imaginary Part of the Atomic Polarizability
• Two-photon approximation in the theory of the electron recombination in hydrogen
• Two-photon decays of highly excited states in hydrogen
• Extension of the sum rule for the transition rates between multiplets to the multiphoton case
• From First Principles of QED to an Application: Hyperfine Structure of P States of Muonic Hydrogen