Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physica Scripta

Theory of Resonance Fluorescence from Vibronic Systems

K.‐E. Süsse, W. Vogel, D.‐G. Welsch

Published Sep 1, 1983• 5 citations
Publisher

Abstract

The problem of resonant interaction between an electromagnetic radiation field and a vibronic system, such as a molecule or a localized electronphonon system, is considered. The vibronic coupling is assumed to result from displaced and distorted potential energy surfaces for the vibrational motion in the electronic quantum states involved in the resonant interaction with the radiation field. Furthermore, the vibrational energy relaxation is taken into account without assumptions about Markovian-type relaxation. In order to study correlation properties of higher than second order in the electric field strength of the light emitted a method of calculation of the expectation value of an arbitrary product combination of effective time evolution operators of the vibronic system is developed. The calculations are performed by utilizing Feynman's disentangling and operator ordering techniques and yield closed solutions in the low-temperature limit. The theory is used for studying the intensity and the normally ordered intensity correlation function of the resonance fluorescence light from a two-atom molecule excited by a relatively weak laser field, which undergoes phase fluctuations. It is shown that the vibronic coupling can give rise to an anticorrelation effect which is substantially stronger than in the case of resonance fluorescence from an atom. For the case of small vibrational damping a general formula which directly connects the asymptotic long-time behaviour of the normalized intensity correlation function with the vibrational relaxation in the molecule is deduced. It should be convenient for the determination of very small vibrational decay rates.

DOI
10.1088/0031-8949/28/3/014

Related papers

Theory of resonance fluorescence from vibronic systems: intensity and intensity correlation

W. Vogel, Th. Ullmann

A nonperturbative treatment of the dynamical behavior of a vibronic system in a resonant, coherent, driving light field is developed. The potential energy surfaces for the vibrational motion in the electronic ground and excited state are assumed to be displaced and distorted relative to one another. A system of three integrodifferential equations is derived from the infinite set of density-matrix equations. Both approximate analytical and numerical solutions are presented for the intensity and the intensity-correlation function of the scattered light. The results are valid for arbitrary ratios of the Rabi frequency to the relaxation rates. A system with fast vibrational relaxation behaves as a two-level system. For systems with slow vibrational relaxation, the applicability of perturbation theory requires pump fields that are weaker than those of a two-level system. The Rabi oscillations occurring in a strong pump field are damped less than those of a two-level system, and the intensity substantially decreases. The long-time behavior (determined by the vibrational relaxation time) is characterized by the increase of the intensity toward its stationary value.

Journal of the Optical Society of America B•Mar 1, 1986•9 citations

Theory of resonance fluorescence from vibronic systems: stationary spectrum

W. Vogel, D.‐G. Welsch

The stationary second-order spectrum of the resonance-fluorescence light from a vibronic system is studied in a nonperturbative manner. In the model used the potential energy surfaces for the vibrational motion in the electronic ground state and in the excited state are assumed to be displaced and distorted relative to each other. The calculations are performed for the case when the frequency of the driving laser field is tuned to the vibrationless electronic transition. In particular, in the high-driving-field limit the vibrationless transition exhibits a triplet structure, the sidebands being narrower and higher in comparison with the well-known two-level case. The Raman lines are shifted and split into doublets, the linewidths being determined by the electronic as well as the vibrational relaxation rates.

Journal of the Optical Society of America B•Dec 1, 1986•4 citations

Resonance fluorescence from vibronic systems with displaced potential-energy surfaces: temporal evolution of the intensity

W. Vogel, D.‐G. Welsch, Harald Kühn

The resonance fluorescence from a vibronic system with displaced potential-energy surfaces is studied. Because of the equal vibrational frequencies in the two electronic quantum states, a large number of vibronic transitions can be excited by a strong laser field. Even in the case of weaker driving fields, nonperturbative effects may be observed provided that the vibrational relaxation is slow enough. If the vibronic coupling is not extremely strong, the Rabi oscillations will arise mainly from the excitation of the vibrationless transition. Furthermore, the damping of the Rabi oscillations may be accompanied by a substantial decrease in intensity.

Journal of the Optical Society of America B•Jan 1, 1988•3 citations

Theory of resonance fluorescence in a fluctuating laser field

W. Vogel, D.‐G. Welsch, K. Wódkiewicz

A method of calculation of multiple-time correlation functions of the resonance fluorescence light from a two-level atom driven by a realistic laser field with phase and amplitude fluctuations is developed. Both kinds of fluctuations are assumed to be Gaussian. The phase fluctuations are treated in the phase-diffusion model. The averaging over the amplitude fluctuations can be performed in a closed way when the relative mean-square amplitude fluctuation is small compared with the ratio of the amplitude correlation decay rate to the characteristic atomic relaxation rate. There is no restriction to Markovian amplitude fluctuations. Arbitrary values for the mean Rabi frequency are allowed. Results are presented for the intensity, the intensity correlation function, and the spectrum of the fluorescent light. It is shown that even in the case when the relative strength of the amplitude fluctuations is small, significant effects can occur due to the finite correlation length of the fluctuations. The results for fast amplitude correlation decay correspond to the situation without amplitude fluctuations. When the correlation time of the amplitude fluctuations becomes comparable with the atomic relaxation times, the Rabi oscillations of the intensity and the intensity correlation function are nearly washed out, and non-Lorentzian line shapes for the side peaks in the spectrum are observed. It is found that the ratio of the heights of the central peak to the side peak increases with increasing correlation time.

Physical Review A•Sep 1, 1983•20 citations

The dependence of the intensity correlation of resonance fluorescence from a molecule on the strength of the pump field

W. Vogel

The intensity correlation behaviour of the resonance fluorescence from a vibronic system is studied, taking into account the effect of the pump radiation on the vibrational relaxation process. It is found that the correlation behaviour changes essentially with the strength of the pump, even if no saturation of the electronic transition occurs.

Journal of Physics B Atomic and Molecular Physics•Dec 14, 1983•8 citations

Resonance fluorescence from linearly coupled vibronic systems: stationary spectrum

H. Kühn, W. Vogel, D.‐G. Welsch

Using the model of displaced potential energy surfaces, we studied the spectrum of the resonance fluorescence light from vibronic systems. In this model, equal vibrational frequencies in the two electronic quantum states allow many vibronic transitions to be in resonance with a monochromatic driving laser field tuned to the electronic transition frequency. Level splittings in the strong-field case give rise to a multiple-line spectrum of the scattered light. In particular, the Rayleigh component consists of a superimposed series of triplets, whereas the Raman part is built up by superimposed quadruplets.

Journal of the Optical Society of America B•Jul 1, 1992•2 citations
The problem of resonant interaction between an electromagnetic radiation field and a vibronic system, such as a molecule or a localized electronphonon system, is considered. The vibronic coupling is assumed to result from displaced and distorted potential energy surfaces for the vibrational motion in the electronic quantum states involved in the resonant interaction with the radiation field. Furthermore, the vibrational energy relaxation is taken into account without assumptions about Markovian-type relaxation. In order to study correlation properties of higher than second order in the electric field strength of the light emitted a method of calculation of the expectation value of an arbitrary product combination of effective time evolution operators of the vibronic system is developed. The calculations are performed by utilizing Feynman's disentangling and operator ordering techniques and yield closed solutions in the low-temperature limit. The theory is used for studying the intensity and the normally ordered intensity correlation function of the resonance fluorescence light from a two-atom molecule excited by a relatively weak laser field, which undergoes phase fluctuations. It is shown that the vibronic coupling can give rise to an anticorrelation effect which is substantially stronger than in the case of resonance fluorescence from an atom. For the case of small vibrational damping a general formula which directly connects the asymptotic long-time behaviour of the normalized intensity correlation function with the vibrational relaxation in the molecule is deduced. It should be convenient for the determination of very small vibrational decay rates.
A nonperturbative treatment of the dynamical behavior of a vibronic system in a resonant, coherent, driving light field is developed. The potential energy surfaces for the vibrational motion in the electronic ground and excited state are assumed to be displaced and distorted relative to one another. A system of three integrodifferential equations is derived from the infinite set of density-matrix equations. Both approximate analytical and numerical solutions are presented for the intensity and the intensity-correlation function of the scattered light. The results are valid for arbitrary ratios of the Rabi frequency to the relaxation rates. A system with fast vibrational relaxation behaves as a two-level system. For systems with slow vibrational relaxation, the applicability of perturbation theory requires pump fields that are weaker than those of a two-level system. The Rabi oscillations occurring in a strong pump field are damped less than those of a two-level system, and the intensity substantially decreases. The long-time behavior (determined by the vibrational relaxation time) is characterized by the increase of the intensity toward its stationary value.
The stationary second-order spectrum of the resonance-fluorescence light from a vibronic system is studied in a nonperturbative manner. In the model used the potential energy surfaces for the vibrational motion in the electronic ground state and in the excited state are assumed to be displaced and distorted relative to each other. The calculations are performed for the case when the frequency of the driving laser field is tuned to the vibrationless electronic transition. In particular, in the high-driving-field limit the vibrationless transition exhibits a triplet structure, the sidebands being narrower and higher in comparison with the well-known two-level case. The Raman lines are shifted and split into doublets, the linewidths being determined by the electronic as well as the vibrational relaxation rates.
The resonance fluorescence from a vibronic system with displaced potential-energy surfaces is studied. Because of the equal vibrational frequencies in the two electronic quantum states, a large number of vibronic transitions can be excited by a strong laser field. Even in the case of weaker driving fields, nonperturbative effects may be observed provided that the vibrational relaxation is slow enough. If the vibronic coupling is not extremely strong, the Rabi oscillations will arise mainly from the excitation of the vibrationless transition. Furthermore, the damping of the Rabi oscillations may be accompanied by a substantial decrease in intensity.
A method of calculation of multiple-time correlation functions of the resonance fluorescence light from a two-level atom driven by a realistic laser field with phase and amplitude fluctuations is developed. Both kinds of fluctuations are assumed to be Gaussian. The phase fluctuations are treated in the phase-diffusion model. The averaging over the amplitude fluctuations can be performed in a closed way when the relative mean-square amplitude fluctuation is small compared with the ratio of the amplitude correlation decay rate to the characteristic atomic relaxation rate. There is no restriction to Markovian amplitude fluctuations. Arbitrary values for the mean Rabi frequency are allowed. Results are presented for the intensity, the intensity correlation function, and the spectrum of the fluorescent light. It is shown that even in the case when the relative strength of the amplitude fluctuations is small, significant effects can occur due to the finite correlation length of the fluctuations. The results for fast amplitude correlation decay correspond to the situation without amplitude fluctuations. When the correlation time of the amplitude fluctuations becomes comparable with the atomic relaxation times, the Rabi oscillations of the intensity and the intensity correlation function are nearly washed out, and non-Lorentzian line shapes for the side peaks in the spectrum are observed. It is found that the ratio of the heights of the central peak to the side peak increases with increasing correlation time.
Using the model of displaced potential energy surfaces, we studied the spectrum of the resonance fluorescence light from vibronic systems. In this model, equal vibrational frequencies in the two electronic quantum states allow many vibronic transitions to be in resonance with a monochromatic driving laser field tuned to the electronic transition frequency. Level splittings in the strong-field case give rise to a multiple-line spectrum of the scattered light. In particular, the Rayleigh component consists of a superimposed series of triplets, whereas the Raman part is built up by superimposed quadruplets.