A complete stochastic theory of relaxation is developed in terms of a homogeneous equation for the averaged density matrix of a system immersed in a thermal bath.\nThis theory is then used as the basis of a new stochastic approach to the phenomenon of collisional broadening of spectral line shapes. Single photon and multiphoton processes are studied.\nThe features of a line shape are linked by simple expressions to the statistical properties of a stochastic hermitian Hamiltonian. The ordinary line shape predicted by Kubo's approach is generalized. The present approach predicts broadening as well as asymmetry and shift. A representation of line shapes in multiphoton processes by diagrams is also developed.A complete stochastic theory of relaxation is developed in terms of a homogeneous equation for the averaged density matrix of a system immersed in a thermal bath.\nThis theory is then used as the basis of a new stochastic approach to the phenomenon of collisional broadening of spectral line shapes. Single photon and multiphoton processes are studied.\nThe features of a line shape are linked by simple expressions to the statistical properties of a stochastic hermitian Hamiltonian. The ordinary line shape predicted by Kubo's approach is generalized. The present approach predicts broadening as well as asymmetry and shift. A representation of line shapes in multiphoton processes by diagrams is also developed.

Dec 1, 19861 citation

Stochastic modelling of relaxation effects in line shapes

Sushanta Dattagupta

Springer eBooksApr 6, 20080 citations

Impact of nonradiative line broadening on emission in photonic and plasmonic cavities

Pavel Ginzburg, Alexey V. Krasavin, David R. Richards +1 more

A light-matter interaction modified by the material environment is one of the central topics in quantum electrodynamics. While a strong coupling between a single emitter and a cavity and the Markovian (exponential) relaxation regime are most straightforwardly covered by theory, real physical systems that include also various line broadening effects may possess a much more complicated behavior. Here we propose a theoretical framework to account for nonradiative interaction effects in emission in photonic and plasmonic cavities. The quantum electrodynamics model formulated via a stochastic Hamiltonian approach has been developed with nonradiative line broadening introduced via the Kubo oscillator model. The impact of competing radiative and nonradiative processes on the emitter dynamics has been studied, showing that nonradiative relaxations, having significant impact on processes in high- $Q$ photonic cavities, are much less influential in the plasmonic regime. The developed theoretical framework is not restricted to the emitter in a cavity example, but represents a general tool for multiple stochastic Hamiltonian evolution, important for various types of interactions where either classical or quantum noise is present.A light-matter interaction modified by the material environment is one of the central topics in quantum electrodynamics. While a strong coupling between a single emitter and a cavity and the Markovian (exponential) relaxation regime are most straightforwardly covered by theory, real physical systems that include also various line broadening effects may possess a much more complicated behavior. Here we propose a theoretical framework to account for nonradiative interaction effects in emission in photonic and plasmonic cavities. The quantum electrodynamics model formulated via a stochastic Hamiltonian approach has been developed with nonradiative line broadening introduced via the Kubo oscillator model. The impact of competing radiative and nonradiative processes on the emitter dynamics has been studied, showing that nonradiative relaxations, having significant impact on processes in high-$Q$ photonic cavities, are much less influential in the plasmonic regime. The developed theoretical framework is not restricted to the emitter in a cavity example, but represents a general tool for multiple stochastic Hamiltonian evolution, important for various types of interactions where either classical or quantum noise is present.

Physical Review AOct 20, 201410 citations

Density-matrix correlations in the relaxation theory of electron broadening

Thomas Gomez, Taisuke Nagayama, David P. Kilcrease +2 more

Spectral lines of radiating atoms are broadened by perturbations due to the surrounding plasma environment. In line-broadening calculations, the statistical average of the perturbation is weighted by the density matrix, which, in thermal equilibrium, contains correlations between the radiator and plasma. These correlations, however, have been neglected by all line-broadening theories except for the kinetic theory. The relaxation theory of line broadening is a mathematically exact derivation containing only one physical approximation: neglect of density-matrix correlations. We revisit this derivation and improve it by including the correlations. The line-broadening operator derived with the updated relaxation theory differs from that derived from the kinetic theory, though both derivations are considered to be exact. The kinetic theory derivation predicts that density-matrix correlations result a strong static shift of spectral lines. Our derivation, on the other hand, predicts that the correlations are a frequency-dependent effect that affects the line wings, and there is no shift of the line due to correlations. In addition, we predict that changes in the line shape due to correlations are only noticeable at extremely high densities. To distinguish the more appropriate model, we compare the shifts calculated with the relaxation and kinetic theory with data. The comparison shows support for the relaxation theory and casts into doubt the accuracy of the derivation of the kinetic theory of line broadening.Spectral lines of radiating atoms are broadened by perturbations due to the surrounding plasma environment. In line-broadening calculations, the statistical average of the perturbation is weighted by the density matrix, which, in thermal equilibrium, contains correlations between the radiator and plasma. These correlations, however, have been neglected by all line-broadening theories except for the kinetic theory. The relaxation theory of line broadening is a mathematically exact derivation containing only one physical approximation: neglect of density-matrix correlations. We revisit this derivation and improve it by including the correlations. The line-broadening operator derived with the updated relaxation theory differs from that derived from the kinetic theory, though both derivations are considered to be exact. The kinetic theory derivation predicts that density-matrix correlations result a strong static shift of spectral lines. Our derivation, on the other hand, predicts that the correlations are a frequency-dependent effect that affects the line wings, and there is no shift of the line due to correlations. In addition, we predict that changes in the line shape due to correlations are only noticeable at extremely high densities. To distinguish the more appropriate model, we compare the shifts calculated with the relaxation and kinetic theory with data. The comparison shows support for the relaxation theory and casts into doubt the accuracy of the derivation of the kinetic theory of line broadening.

Physical Review AJul 16, 201810 citations

Stochastic Optics

Luis de la Peña, Ana Marı́a Cetto

Springer eBooksJan 1, 19960 citations

Q

photonic cavities, are much less influential in the plasmonic regime. The developed theoretical framework is not restricted to the emitter in a cavity example, but represents a general tool for multiple stochastic Hamiltonian evolution, important for various types of interactions where either classical or quantum noise is present.