Interference effects in step-wise fluorescence due to level-crossings

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.