One- vs. Three-Photon Interference

The probability to produce fragments q at a fixed energy E is therefore 

Recognizing that e, is a complex number, , = i e f, we can write the above J interference term as 

The numerator and denominator of Eq. (3.54) each display the canonical form for coherent control, that is, a form similar to Eq. (3.19) in which there are independent contributions from more than one route, modulated by an interference term. Since the interference term is controllable through variation of the (x and / 3 — 3 / ,) laboratory parameters, so too is the branching ratio Rqq,(E). Thus, the principle upon which this control scenario is based is the same as that in Section 3.1, but the interference is introduced in an entirely different way. 

Three Dimensional Formalism With the qualitative principle of interfering pathways exposed, it remains to demonstrate the quantitative extent to which the one- vs. three-photon scenario alters the yield ratio in a realistic system. To this end we consider the photodissociation of IBr, 

Because we want to consider the one- vs. three-photon control of IBr in three, dimensions [63], we replace the notation Z () for the initial state by Ef,Mt), s here Et is, as before, the energy of the state, J, is its angular momentum, and is the angular momentum projection along the z axis. Where no confusion arises, i ffe continue to use Et) for simplicity. 

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