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Journal of the Optical Society of America B

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

W. Vogel, D.‐G. Welsch, Harald Kühn

Published Jan 1, 1988• 3 citations
Publisher

Abstract

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.

DOI
10.1364/josab.5.000067

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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 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.
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.
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.
We study theoretically the Rabi oscillations of a resonantly driven two-level system linearly coupled to a harmonic oscillator (vibrational mode) with frequency ${\ensuremath{\omega}}_{0}$. We show that for weak coupling, ${\ensuremath{\omega}}_{p}\ensuremath{\ll}{\ensuremath{\omega}}_{0}$, where ${\ensuremath{\omega}}_{p}$ is the polaronic shift, Rabi oscillations are strongly modified in the vicinity of the Rabi-vibronic resonance ${\ensuremath{\Omega}}_{R}={\ensuremath{\omega}}_{0}$, where ${\ensuremath{\Omega}}_{R}$ is the Rabi frequency. The width of the resonance is $({\ensuremath{\Omega}}_{R}\ensuremath{-}{\ensuremath{\omega}}_{0})\ensuremath{\sim}{\ensuremath{\omega}}_{p}^{2/3}{\ensuremath{\omega}}_{0}^{1/3}\ensuremath{\gg}{\ensuremath{\omega}}_{p}$. Within this domain of ${\ensuremath{\Omega}}_{R}$ the actual frequency of the Rabi oscillations exhibits a bistable behavior as a function of ${\ensuremath{\Omega}}_{R}$. Importantly, within the resonant domain, the oscillator is highly excited, which allows us to treat it classically.