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Physical Review A

Quantum interference between resonant and nonresonant contributions in nearly resonant Raman scattering

Shuichi Kinoshita, Takashi Kushida

Published Sep 1, 1990• 5 citations
Publisher

Abstract

Time-resolved secondary-radiation spectra have been calculated for a three-level system coupled with a reservoir under pulsed-light excitation. It has been found that a dip is observed in the time profile of the secondary-radiation intensity near the resonance-excitation condition, when the spectral bandwidth of the detection system is increased. If the secondary radiation is divided into the Raman and luminescence components that are, respectively, due to the mean value and fluctuation of the photoinduced emission dipole, the dip is observed only in the former. A simple analysis reveals that this dip originates from the quantum interference between the resonant and nonresonant contributions to the Raman scattering.

DOI
10.1103/physreva.42.2751

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Time-resolved secondary-radiation spectra have been calculated for a three-level system coupled with a reservoir under pulsed-light excitation. It has been found that a dip is observed in the time profile of the secondary-radiation intensity near the resonance-excitation condition, when the spectral bandwidth of the detection system is increased. If the secondary radiation is divided into the Raman and luminescence components that are, respectively, due to the mean value and fluctuation of the photoinduced emission dipole, the dip is observed only in the former. A simple analysis reveals that this dip originates from the quantum interference between the resonant and nonresonant contributions to the Raman scattering.
Various characteristics of frequency-integrated intensities of secondary radiation components near the resonance excitation region have been calculated for a three-level system coupled with a reservoir using a stochastic model. It has been found that the spectral and temporal characteristics of the resonant second-order optical processes can be understood consistently by considering that Raman scattering results from the average value of the induced-dipole moment with respect to the energy fluctuation due to the system-reservoir interaction, while luminescence results from its deviation from the average value. A simple method to determine parameter values that characterize the excited-state dynamics in condensed phases from the secondary radiation data is also discussed.
The perturbative density matrix formalism is used to study the time-dependent resonance Raman scattering (RRS) and resonance hot luminescence (RHL) components of the light-induced spontaneous emission process that has been called resonance secondary radiation (RSR). A three-level system coupled in a stochastic way to a bath is used to study the RSR emission driven by a coherent laser pulse with a variable Gaussian width in time. The spectral filter in a light detection system is explicitly included in the detection step of the problem. Observable time and frequency resolved RSR spectra are then calculated numerically. The spectral and temporal properties of the time-dependent RSR spectrum are very sensitive to the width of the driving pulse when the pulse width is of the same order of magnitude as the important system dephasing constants. In this domain the RRS contribution to the RSR spectrum weakens relative to the RHL as the light pulse is shortened. In the limit that the laser pulse becomes ‘‘delta function-like’’ the RSR spectrum consists essentially of RHL. When appropriate, the numerical results are compared to the stationary RSR problem as well as to the case where the RSR emission is driven by an exponential pulse. The analytical solutions to both of these cases are presented.
The effects of the finite correlation time of the external modulation on the secondary-emission spectra are clarified emphasizing the deviation from the motional narrowing limit or the impact approximation in the case of large off-resonance excitation. The dependences of the excitation spectrum of the secondary emission on the modulation parameters and on the inhomogeneous broadening are studied systematically. It is found that the excitation spectrum of the luminescence shows a faster decrease than that of the Raman scattering as the off-resonance frequency increases. The present theory is relevant for explaining the recent experiment by Watanabe, Kinoshita, and Kushida [Chem. Phys. Lett. 126, 197 (1986)] on the \ensuremath{\beta}-carotene in solutions. A general theory of the time-resolved spectra of the secondary emission is formulated to incorporate the effect of the finite correlation time. The luminescence component shows a slow temporal decay with the longitudinal relaxation rate. It is found for the first time that the difference is unexpectedly large between the transient behavior of the luminescence intensity and that of the intermediate-state population for the slow-modulation regime and that the difference indicates the effect of finite correlation time of the frequency modulation. On the other hand, the transient behavior of the Raman scattering contains a fast component that follows the envelope of the excitation-pulse intensity and the same slow component as the luminescence. The ratio of the slow component to the total intensity depends sensitively on the modulation parameters and the off-resonance frequency. The modulation parameters of the system in question can be estimated from these dependences in combination with the spectral characteristics of the emission under stationary excitation.
The approximation of nonoverlapping lines is used to calculate spectra of resonance fluorescence and Raman scattering when two- and three-level atoms are pumped by a smooth pulse of duration comparable with the excited-state lifetime. The difference between the quasienergy terms, that determines the satellite frequency, depends on time and has the same value twice, at the pulse leading and trailing edges, so that interference may occur between the radiation produced in the appropriate parts of the pulse. However, the interference pattern is blurred since radiative broadening destroys the coherence. Relationships are obtained between the parameters for which interference may be observed. An analysis is made of the change to short pulses when allowance can be made for the scattered field using the first order of perturbation theory.
Resonance Raman scattering and luminescence under an intense excitation field are studied for both stationary and transient excitation regimes. By means of the Green function theory of resonance Raman scattering and luminescence we explain the characteristic features of the recent experiments on two-photon resonance Raman scattering via excitonic molecule in CuCl where the resonance dip and the asymmetry of the Raman yield around the resonance were observed. We ascribe the origin of the resonance dip of the Raman yield to the resonance enhancement of collisional damping of excitonic molecule and exciton states. The asymmetry of the Raman yield can be naturally understood in terms of the frequency and wave-vector dependent relaxation constants. Furthermore an approach is proposed which incorporates the coherence and correlation among excitonic molecules and excitons in their non-equilibrium state and clarifies their effects on the optical spectra.
Time-dependent spectra of light emitted after two-photon excitation with nonresonant intermediate state are studied by the perturbation method. Two components are distinguished: a slow one Is{I}_{s}Is​ connected with the excited-state population, and a fast one If{I}_{f}If​ connected with the double-quantum optical coherence. For large detuning of the two-photon frequency from the excited-ground-state energy separation, the fluorescent light is found to be ${I}_{s}\ensuremath{-}|{I}_{f}|$, and the Raman-scattered light is If{I}_{f}If​. The influence of statistics of light, laser linewidth, spectral bandwidth of the detector, and transfer of coherence from the ground to the excited state are also taken into consideration.