Quantum electrodynamics of resonant energy transfer in condensed matter

A microscopic many-body QED theory for dipole-dipole resonance energy transfer has been developed from first principles. A distinctive feature of the theory is full incorporation of the dielectric effects of the supporting medium, in the context of an interplay between what have traditionally been regarded as radiationless and radiative excitation transfer. The approach employs the concept of bath polaritons mediating the energy transfer. The transfer rate is derived in terms of the Green’s operator corresponding to the polariton matrix Hamiltonian. In contrast to the more common lossless polariton models, the present theory accommodates an arbitrary number of energy levels for each molecule of the medium. This includes, in particular, a case of special interest, where the excitation energy spectrum of the bath molecules is sufficiently dense that it can be treated as a quasicontinuum in the energy region in question, as in the condensed phase normally results from homogeneous and inhomogeneous line broadening. In such a situation, the photon ‘‘dressed’’ by the medium polarization (the polariton) acquires a finite lifetime, the role of the dissipative subsystem being played by bath molecules. It is this which leads to the appearance of the exponential decay factor in the microscopically derived pair transfer rates. Accordingly, the problem associated with potentially infinite total ensemble rates, due to the divergent ${\mathit{R}}^{\mathrm{-}2}$ contribution, is solved from first principles. In addition, the medium modifies the distance dependence of the energy transfer function A(R) and also produces extra modifications due to screening contributions and local field effects. The formalism addresses cases where the surrounding medium is either absorbing or lossless over the range of energies transferred. In the latter case the exponential factor does not appear and the dielectric medium effect in the near zone reduces to that which is familiar from the theory of radiationless (Förster) energy transfer.