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

Abstract

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.

Controlling resonance energy transfer in nanostructure emitters by positioning near a mirror

“…nient to model EM waves using a Hankel function of order n. 25,54,55 In a similar manner to the previous case in Sec.III A, if µ(D), µ(A) are oriented in the positive x direction and two nanowires are located along the z axis (Rx = 0) as shown in Fig.4(a), then we have…”

“…25,55 Therefore, by imposing the limits (zD → ∞), we can successfully simplify the mirror-assisted RET to the no-mirror case (direct RET). The magnitude of the quantum amplitude in the absence of the mirror becomes µ…”

Manipulating nanoscale atom–atom interactions with cavity QED

“…The initial state Ψ(0) is a product of internal and external motional state of the two atoms. Equation (20) describe the coherent evolution of the system.…”

Electric dipole coupling in optical cavities and its implications for energy transfer, up-conversion, and pooling

“…Within the abstraction of reduced dimensionality, for instance, this is certainly the case 19,20 . Twodimensional RET has an R −4 near-field fall off with separation, while its one-dimensional counterpart is not sensitive to separation at all.…”

“…The coupling expressions derived are intended to be helpful in designing systems that optimize the efficiency of desired excitonic processes relative to other relaxation channels that may be available. They are also relevant in the exploration of RET, ETU and EP analogs to Dicke superradiance in cavities 25 and as a reference point when considering excitonic dynamics within the strong coupling regime 19 . The methodology developed can be used to quantify exciton dynamics in plasmonic grating settings as well.…”