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Physical Review

"Anticrossing" Signals in Resonance Fluorescence

Harold Wieder, T. G. Eck

Published Jan 5, 1967• 125 citations
Publisher

Abstract

The level-crossing technique of atomic spectroscopy utilizes the spatial interference in the scattering of resonance radiation which can occur when two Zeeman levels of an atom are brought into coincidence ("crossed") by the application of an external magnetic field. "Anticrossing" refers to the case where the two levels involved are coupled by a small static interaction. In this paper the general expression for an anticrossing signal is given and its predictions compared with signals observed in the $2 ^{2}P$ term of Li. It is shown that anticrossings produce signals in many experimental situations for which there would be no signal from a normal level crossing.

DOI
10.1103/physrev.153.103

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Interference of diffusing photons and level crossing spectroscopy

Éric Akkermans, Ohad Assaf

We show that a new interference effect appears in the intensity fluctuations of photons multiply scattered by an atomic gas of large optical depth b. This interference occurs only for scattering atoms that are Zeeman degenerate and it leads to a deviation from the Rayleigh law. The fluctuations measured by their variance, display a resonance peak as a function of an applied magnetic field. The resonance width is proportional to the small factor 1/b. We derive closed analytic expressions for all these physical quantities which are directly accessible experimentally.

arXiv:cond-mat/0610454•Oct 17, 2006•0 citations
The level-crossing technique of atomic spectroscopy utilizes the spatial interference in the scattering of resonance radiation which can occur when two Zeeman levels of an atom are brought into coincidence ("crossed") by the application of an external magnetic field. "Anticrossing" refers to the case where the two levels involved are coupled by a small static interaction. In this paper the general expression for an anticrossing signal is given and its predictions compared with signals observed in the 22P2 ^{2}P22P term of Li. It is shown that anticrossings produce signals in many experimental situations for which there would be no signal from a normal level crossing.
We report the observation of anticrossing signals arising from the interaction of 300-K blackbody radiation with Rydberg atoms near avoided crossings of Stark levels. The role of the blackbody radiation is roughly analogous to that of the resonance fluorescence in traditional anticrossing spectroscopy. We present preliminary results for avoided crossings of ns\mathrm{ns}ns states with $n\ensuremath{-}2$ Stark states in potassium for nnn in the range 18-21.
An interaction Hamiltonian analogous to that in a coupled Lee model is used to calculate the transition matrix appropriate for the description of the anticrossing effect in optical resonance fluorescence. The transition matrix is found to contain two terms (in addition to those for resonance scattering through each of the coupled states) which exist in the amplitude only because the damping matrix in the coupled representation is not diagonal. This matrix is diagonal when the uncoupled states have equal radiative widths, and the resonance scattering intensity is then given by the Breit formula. This result justifies the application by Eck, Foldy, and Wieder of the Breit equation to their initial discovery of the anticrossing effect even though this formula would not be expected to apply to the general anticrossing situation. The crossing effect can also be discussed as a special case of the approach presented.
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.
We show that a new interference effect appears in the intensity fluctuations of photons multiply scattered by an atomic gas of large optical depth b. This interference occurs only for scattering atoms that are Zeeman degenerate and it leads to a deviation from the Rayleigh law. The fluctuations measured by their variance, display a resonance peak as a function of an applied magnetic field. The resonance width is proportional to the small factor 1/b. We derive closed analytic expressions for all these physical quantities which are directly accessible experimentally.