A retarded coupling approach to intermolecular interactions

Abstract

A wide range of physical phenomena such as optical binding and resonance energy transfer involve electronic coupling between adjacent molecules. A quantum electrodynamical description of these intermolecular interactions reveals the presence of retardation effects. The clarity of the procedure associated with the construction of the quantum amplitudes and the precision of the ensuing results for observable energies and rates are widely acknowledged. However, the length and complexity of the derivations involved in such quantum electrodynamical descriptions increase rapidly with the order of the process under study. Whether through the use of time-ordering approaches, or the more expedient state-sequence method, time-consuming calculations cannot usually be bypassed. A simple and succinct method is now presented, which provides for a direct and still entirely rigorous determination of the quantum electrodynamical amplitudes for processes of arbitrarily high order. Using the approach, new results for optical binding in two-and three-particle systems are secured and discussed.

Enhancing Optical Up-Conversion Through Electrodynamic Coupling with Ancillary Chromophores

“…By convention, superscript labels associated with the electronic dipole moments read from right to left, implementing the general notation μ fi (ξ) = ⟨ξ f | μ |ξ i ⟩. Equation features the fully retarded, second-rank dipole–dipole coupling tensor V ij ( k , R AA ′ ), − cast in terms of the interchromophore displacement R in the following expression: As previously established, the square modulus of M FI ( AA ′) is required to determine the UC rate and as a means to keep the presented results general and not otherwise restricted to the description of fixed and/or highly ordered systems, chromophores are assumed at all times to be randomly orientated in three dimensions, thus where angular brackets denote the required operation of a rotational average. An integration-free procedure based on isotropic matrix elements is subsequently utilized, , eq requiring both second- and fourth-rank tensor averages, the former presented in the following general form: in which ⟨ iλ jμ ⟩ represents a product of direction cosines.…”

The effect of scattering on single photon transmission of optical angular momentum

“…There are twenty four individual, topologically distinct time-orderings that contribute to the overall matrix element for the process [61]-corresponding to twenty four Feynman graphs of the form illustrated in figure 1(c). The underlying motifs of the scattering and energy transfer representations, figures 1(a) and (b), are plainly evident, but it is to be emphasized that the energy transferred between the two centres, in the case of double scattering, is determined by the input, having no correlation with any individual electronic state of either A or B.…”

Multiple light scattering and optomechanical forces

“…Based on the coupling method described in ref. [27], the resulting optically induced energy between the interacting centers emerges as follows:…”

“…N radiation state-sequences -for example, in the case of a three-center system this would involve consideration of 6 different mechanisms each involving 720 paths, each one cast as a different route through the corresponding statesequence graph. Fortunately, a recently published coupling method [27] offers a straightforward answer to such a problem. This method can deliver a result for a system with an unspecified number of centers.…”

“…In particular, for the simplest case of a threecenter system, first studied in ref. [27], we have contributions of the form: …”