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The Journal of Chemical Physics

Cooperative radiation accompanying photon-exchange interaction between neighboring atoms

Samuel H. Brown, Ying‐Nan Chiu, V. Sethu Raman

Published Dec 1, 1976• 0 citations
Publisher

Abstract

The radiative processes involving two interacting neutral atomic systems are studied by the third-order scattering matrix formalism of modern quantum electrodynamics. Two bound electrons on different nuclei are allowed to interact through the exchange of scalar, longitudinal, and transverse photons and one system either emits or absorbs radiation in a one-photon process. The third-order S-matrix is reduced to the U-matrix which is rigorously evaluated in the nonrelativistic limit. This evaluation produces new radiative interaction transition operators which are different from those obtained by earlier investigators. These new radiative transition operators presented here should be useful for studying molecular interactions producing cooperative optical phenomena.

DOI
10.1063/1.433001

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The radiative processes involving two interacting neutral atomic systems are studied by the third-order scattering matrix formalism of modern quantum electrodynamics. Two bound electrons on different nuclei are allowed to interact through the exchange of scalar, longitudinal, and transverse photons and one system either emits or absorbs radiation in a one-photon process. The third-order S-matrix is reduced to the U-matrix which is rigorously evaluated in the nonrelativistic limit. This evaluation produces new radiative interaction transition operators which are different from those obtained by earlier investigators. These new radiative transition operators presented here should be useful for studying molecular interactions producing cooperative optical phenomena.
The two-photon and scattering resonances between the spontaneous emissions of the two- and single- photon transitions of the three-level inverted radiators in the Ξ, V configurations and the system of two-level radiators D, inverted relatively the dipole forbidden transition are revised. This approach opens the new possibilities in the manipulation of the decay process and generation of the entangled photon pairs. The correlation between the V and Ξ cascade three-level subsystems on the two-photon transitions of dipole forbidden radiators is studied, taking into consideration the cooperative scattering and two photon resonances through the vacuum field. One of them corresponds to the situation when the total energy of emitted photons by three level dipole-active radiator in the cascade configuration enters into the two-photon resonance with the dipole-forbidden transitions of second atom. Another effect corresponds to the scattering situation, when the difference of the excited energies of the two dipole-active transitions of V three level radiator are in the resonance with the dipole-forbidden transitions of the second one. These effects are accompanied with the interferences between single- and two-quantum collective transitions of the inverted radiators from the ensemble. The two particle collective decay rate is defined in the description of the atomic correlation functions.
A landmark in the development of quantum electrodynamics was the discovery that emission–reabsorption of virtual photons modifies the value of energy levels in an atom from those computed by using Dirac’s equation (Lamb shift). An early result of statistical quantum electrodynamics was that the exchange of virtual photons in an ensemble of identical atoms leads as well to a change in the frequency of the radiation emitted from this system (cooperative Lamb shift). Dicke’s discovery that coherence effects lead to the shortening of the emission lifetime from a small sample by a factor equal to the number of atoms in the ensemble (superradiance or cooperative decay rate) was an early landmark in quantum optics. Both cooperative decay rate and cooperative Lamb shift were shown to have the same physical origin—the exchange of virtual photons, a process described by the Lienard–Wiechert dipole–dipole interaction. This effective potential is the kernel of the integral equation describing the dynamics of the system. This complex long-range kernel gives, for both cooperative quantities, strong dependence on the geometry of the atomic cloud. I summarize the known expressions for the initial cooperative decay rate and the cooperative Lamb shift in different geometries. The results for both the scalar photon and the vector photon (electrodynamics) theories for experimentally realizable systems of either uniform or phased polarization are given.
Abstract The quantum electrodynamic theory, based on the quantization of the electromagnetic field, introduces the concept of photon and the related photon creation operator, photon annihilation operator, and photon number operator. It is used to describe stimulated Raman scattering, stimulated Kerr scattering, and various multiphoton excitation processes. Within this theoretical regime the light (as a photon field) and molecules are treated as a combined quantum mechanical system. The light emission or absorption is always accompanied by the quantum transition of the whole system from its initial eigenstate to the final eigenstate. The molecular emission or absorption probability rate is determined by the corresponding transition matrix elements of the interaction Hamiltonian operator.
The resonances between the spontaneous and induced emissions by two- and single photon transitions of three inverted radiators from the ensemble proposed in paper45 open the new possibilities in the manipulation of the decay rate of the entangled photon pairs generated by the system relative the dipole-forbidden transition. The influence of the bath temperature to such process is studied. One of them corresponds to the situation when the total energy of emitted photons by two dipole-active radiators enter the two-photon resonance with the dipoleforbidden transitions of third atom. Second effect corresponds to the scattering situation, when the difference of the excited energies of two dipole-active radiators are in the resonance with the dipole-forbidden transitions of third atom. These effects are accompanied with the interferences between single- and two-quantum collective transitions of three inverted radiators from the ensemble. The three particle collective decay rate is defined in the description of the atomic correlation functions. © (2012) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
The collective decay effects between the dipole-active three-level subsystems in the nonlinear interaction with dipole-forbidden transitions, like 2 S − 1 S of hydrogen-like radiators, are proposed, taking into consideration the cooperative exchanges between two species of atoms through the vacuum field in the scattering and the two-photon resonance processes. One of them corresponds to the situation when the total energy of the emitted two photons by the three-level radiator in the cascade configuration enters into the two-photon resonance with another type of dipole-forbidden transitions of hydrogen-like (or helium-like) atoms. The similar situation appears in the cooperative scattering between two species of quantum emitters when the difference of the excited energies of the two dipole-active transitions of the three-level radiators is in the resonance with the dipole-forbidden transitions of the Hydrogen-like radiators. These effects are accompanied by the interference between single- and two-quantum collective transitions of the inverted radiators from the ensemble. The two-particle collective decay rate is defined in the description of the atomic correlation functions taking into consideration the phase retardation between them. The kinetic equations which describe the cooperative processes as the function of time and correlation are obtained. The behavior of the system of radiators at short and long time intervals in comparison with the retardation time between them is studied.