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Bulletin of the American Physical Society

Interference between two resonant transitions with distinct initial and final states connected by radiative decay

Eric A. Hessels, Marko Horbatsch, A. Marsman

Published May 31, 2018• 0 citations
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The semi-classical derivation of the Kramers-Heisenberg formula describing resonance scattering is extended to the step-wise scattering of light. We consider an atom (such as 198 Hg) which interacts with two polarized beams of light (λ2537 Å and λ4358 Å): starting from a specific initial state 0 (6 1 S 0 ), it undergoes a two-step excitation (6 1 S 0 → 6 3 P 1 → 7 3 S 1 ), and makes a transition to one specific final state F (any magnetic sub-state of the 6 3 P 2.1.0 terms). It thus emits step-wise radiation (λ5461 Å or λ 4358 Å or λ4047 Å). A possible route 0 → r → r' → F taken by the atom in the scattering process is defined by two possible intermediate states (r', r). When there are two routes connecting 0 to F, the fluorescent intensity observed through an analyser differs from that obtained by adding the corresponding transition rates, owing to a quantum-mechanical interference term. Observations on the fluorescent intensity from 198 Hg vapour as a function of applied magnetic field confirm three types of interferences, occurring at the zero-field crossing of Zeeman sub-levels. The first is analogous to that observed in resonance fluorescence. Two new types are (i) a level-crossing signal essentially in the absorption of the second radiation, due to degeneracy of states excited in the first term (6 3 P 1 ), and (ii) a multiplicative level-crossing signal, where mutual coherence between one pair of degenerate states excited in the first step is carried over to a second pair in the next step.

Proceedings of the Physical Society•Dec 1, 1965•23 citations
The fluorescence produced by an autoionizing state under strong pumping by a coherent laser field is considered. It is shown how the spectrum of emitted photons and the total number of photons are related to the two-time and single-time atomic expectation values, and explicit expressions are derived for them. Numerical results for the time development of the number of photons ejected are presented for finite times and in the long-time limit. The photon spectra are shown to exhibit ac Stark splitting of the states involved. The spectrum is a doublet for transitions to a stable final state and a triplet for transitions connected back to the initial, strongly driven state. The decay of an autoionizing state in the absence of a laser driving field is considered, and the square of the Fano qqq value is interpreted as the ratio of two decay rates.
The semi-classical derivation of the Kramers-Heisenberg formula describing resonance scattering is extended to the step-wise scattering of light. We consider an atom (such as 198 Hg) which interacts with two polarized beams of light (λ2537 Å and λ4358 Å): starting from a specific initial state 0 (6 1 S 0 ), it undergoes a two-step excitation (6 1 S 0 → 6 3 P 1 → 7 3 S 1 ), and makes a transition to one specific final state F (any magnetic sub-state of the 6 3 P 2.1.0 terms). It thus emits step-wise radiation (λ5461 Å or λ 4358 Å or λ4047 Å). A possible route 0 → r → r' → F taken by the atom in the scattering process is defined by two possible intermediate states (r', r). When there are two routes connecting 0 to F, the fluorescent intensity observed through an analyser differs from that obtained by adding the corresponding transition rates, owing to a quantum-mechanical interference term. Observations on the fluorescent intensity from 198 Hg vapour as a function of applied magnetic field confirm three types of interferences, occurring at the zero-field crossing of Zeeman sub-levels. The first is analogous to that observed in resonance fluorescence. Two new types are (i) a level-crossing signal essentially in the absorption of the second radiation, due to degeneracy of states excited in the first term (6 3 P 1 ), and (ii) a multiplicative level-crossing signal, where mutual coherence between one pair of degenerate states excited in the first step is carried over to a second pair in the next step.