Resonant dipole–dipole interaction in confined and strong-coupling dielectric geometries

Using the electromagnetic response function of an electric dipole located within a dielectric geometry, we derive the mathematical equivalence between the classical response and quantum mechanical resonant dipole–dipole interaction between two quantum objects (atoms, quantum dots, etc). Cooperative spontaneous emission likewise emerges from this equivalence. We introduce a practical numerical technique using finite difference time domain for calculating both dipole–dipole interaction and collective spontaneous emission in confined dielectric structures, where strong light–matter coupling might arise. This method is capable of obtaining resonant dipole–dipole interaction over a wide range of frequencies in a single run. Our method recaptures the results of quantum mechanical second order perturbation theory for weak light–matter coupling. In strong coupling situations such as near a photonic band edge, second order Rayleigh–Schrödinger perturbation theory leads to divergences, and instead Brillouin–Wigner perturbation theory is required. This is equivalent to the use of a variational wavefunction to describe the exciton transfer between initial and final states. We introduce a system of coupled classical oscillators, that describes resonant dipole–dipole interaction and vacuum Rabi splitting in the strong-coupling regime, and that provides an effective numerical scheme based on the finite difference time domain method. This includes the effects of quantum entanglement and the correlation of quantum fluctuations. We discuss the crossover to Forster energy transfer when quantum correlations between the dipoles are damped by strong environmental interactions. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New Journal of Physics 15 (2013) 083033 1367-2630/13/083033+28$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft