Relation of Crossing and Anticrossing Effects in Optical Resonance Fluorescence

Abstract

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.