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Physical Review A

Intermolecular forces, spontaneous emission, and superradiance in a dielectric medium: Polariton-mediated interactions

Jasper Knoester, Shaul Mukamel

Published Dec 1, 1989• 128 citations

Abstract

A reduced equation of motion that describes the excited-state dynamics of interacting two-level impurity molecules in a dielectric host crystal is derived starting from a microscopic model for the total system. Our theory generalizes the derivation of the conventional superradiance master equation for molecules in vacuum; the role of photons in the conventional theory is played by polaritons (mixed crystal-radiation excitations) in our approach. Our final equation thus contains dispersive and superradiant polariton-mediated intermolecular interactions. The effect of the dielectric host is completely contained within a rescaling of these interactions with the transverse dielectric function \ensuremath{\epsilon}(\ensuremath{\omega}) of the crystal taken at the impurity's transition frequency. Our theory yields all local field and screening factors for both the dispersive and the dissipative couplings from a single, unified starting point. Known scaling laws for the spontaneous-emission rate and the instantaneous dipole-dipole interaction are extended to the frequency region where the dispersion of \ensuremath{\epsilon}(\ensuremath{\omega}) is important.

DOI: 10.1103/physreva.40.7065

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A reduced equation of motion that describes the excited-state dynamics of interacting two-level impurity molecules in a dielectric host crystal is derived starting from a microscopic model for the total system. Our theory generalizes the derivation of the conventional superradiance master equation for molecules in vacuum; the role of photons in the conventional theory is played by polaritons (mixed crystal-radiation excitations) in our approach. Our final equation thus contains dispersive and superradiant polariton-mediated intermolecular interactions. The effect of the dielectric host is completely contained within a rescaling of these interactions with the transverse dielectric function \ensuremath{\epsilon}(\ensuremath{\omega}) of the crystal taken at the impurity's transition frequency. Our theory yields all local field and screening factors for both the dispersive and the dissipative couplings from a single, unified starting point. Known scaling laws for the spontaneous-emission rate and the instantaneous dipole-dipole interaction are extended to the frequency region where the dispersion of \ensuremath{\epsilon}(\ensuremath{\omega}) is important.

The dynamics of a collection of resonant atoms embedded inside an inhomogeneous nondispersive and lossless dielectric is described with a dipole Hamiltonian that is based on a canonical quantization theory. The dielectric is described macroscopically by a position-dependent dielectric function and the atoms as microscopic harmonic oscillators. We identify and discuss the role of several types of Green tensors that describe the spatio-temporal propagation of field operators. After integrating out the atomic degrees of freedom, a multiple-scattering formalism emerges in which an exact Lippmann-Schwinger equation for the electric field operator plays a central role. The equation describes atoms as point sources and point scatterers for light. First, single-atom properties are calculated such as position-dependent spontaneous-emission rates as well as differential cross sections for elastic scattering and for resonance fluorescence. Secondly, multiatom processes are studied. It is shown that the medium modifies both the resonant and the static parts of the dipole-dipole interactions. These interatomic interactions may cause the atoms to scatter and emit light cooperatively. Unlike in free space, differences in position-dependent emission rates and radiative line shifts influence cooperative decay in the dielectric. As a generic example, it is shown that near a partially reflecting plane there is a sharp transition from two-atom superradiance to single-atom emission as the atomic positions are varied.

Resonant classical light scattering by impurity atoms inside dielectric cubic lattices is investigated in the point-dipole limit. Modifications to resonance frequencies and linewidths are shown to be different for substitutional and interstitial impurities. Spontaneous emission rates inside dielectrics exhibit the well-known empty-cavity and Lorentz local-field factors for substitutional and interstitial atoms, respectively. The results are generalized to disordered dielectrics, indicating that the substitutional case occurs prevalently for impurity atoms.

Decay of an excited molecule (atom) has been considered in an absorbing dielectric. The decay rate has been derived calculating the total rate of excitation transfer to the surrounding species. The contribution due to the far-zone energy transfer yields the rate of photon emission in the absorbing medium. The analysis is based on a microscopic QED theory of energy transfer in condensed phases. As a result, effects due to discreteness of the medium (such as the local field effects) are reflected intrinsically in the decay rates. The microscopic approach supports the previous introduction of the local field factors on a phenomenological basis.

Decay of an excited molecule ~atom! has been considered in an absorbing dielectric. The decay rate has been derived calculating the total rate of excitation transfer to the surrounding species. The contribution due to the far-zone energy transfer yields the rate of photon emission in the absorbing medium. The analysis is based on a microscopic QED theory of energy transfer in condensed phases. As a result, effects due to discreteness of the medium ~such as the local field effects! are reflected intrinsically in the decay rates. The microscopic approach supports the previous introduction of the local field factors on a phenomenological basis.

In this study, we present the superradiance effects of N identical molecular emitters inside Fabry–Pérot (FP) cavity systems in the framework of macroscopic quantum electrodynamics. The proposed theory can estimate the enhancement of spontaneous emission rates, including the effects of cavity geometry and material dielectric properties. Moreover, our study connects the multichromophoric excitation energy transfer theory and the Tavis–Cummings model via identical cooperative decay rates and dipole–dipole shifts. For molecules resonant with the cavity photon mode, we find that the enhancement is not exactly proportional to N even in a perfect FP cavity due to the effects of electrostatic dipole–dipole interactions. Moreover, in a silver FP cavity, our simulation shows that the enhancement saturates for a large N, indicating that the cavity photon mode can lead to only the collective emission of a limited number of molecules. For molecules in the proximity of the silver mirror, we demonstrate that under specific conditions, the subradiance of molecular emitters can occur through surface plasmon polaritons. Our study not only provides new insights into the mechanism of superradiance effects but also demonstrates that collective effects such as superradiance and subradiance can be controlled by manipulating the dielectric environments.