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Physical Review A

Non-Markovian effect in resonant light scattering: Time-resolved spectrum

Michio Hama, Masaki Aihara

Published Jun 1, 1987• 9 citations
Publisher

Abstract

We present a theoretical work on non-Markovian effects in the time-resolved spectrum (TRS) of resonant light scattering caused by a short pulse excitation. It is found that when the off-resonance frequency becomes comparable or greater than the inverse of the reservoir correlation time ${\ensuremath{\tau}}_{c}$, the finiteness of ${\ensuremath{\tau}}_{c}$ reduces the luminescencelike component which is energetically and temporally uncorrelated with incident radiation. It is emphasized that this non-Markovian effect in TRS is essential for obtaining a full understanding of the resonant light scattering phenomena.

DOI
10.1103/physreva.35.4842

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We present a theoretical work on non-Markovian effects in the time-resolved spectrum (TRS) of resonant light scattering caused by a short pulse excitation. It is found that when the off-resonance frequency becomes comparable or greater than the inverse of the reservoir correlation time \ensuremathτc{\ensuremath{\tau}}_{c}\ensuremathτc​, the finiteness of \ensuremathτc{\ensuremath{\tau}}_{c}\ensuremathτc​ reduces the luminescencelike component which is energetically and temporally uncorrelated with incident radiation. It is emphasized that this non-Markovian effect in TRS is essential for obtaining a full understanding of the resonant light scattering phenomena.
Time-resolved resonant light scattering in a disordered system is theoretically investigated. It is found that pulse excitation enables one to observe directly the relaxation of elementary excitations which is caused by disorder. In the case of weak disorder, the rapid scatteringlike and slow luminescencelike components distinctively appear. In the case of strong disorder, a continuous change from scattering to luminescence appears, which reflects the dephasing dynamics in the excited states of a disordered system.
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 dependence of the electronic absorption spectrum of a dye molecule on the time of delay between the excitation of the molecule by a pump-laser pulse and the probing of the absorption by a test-laser pulse is studied. The effect of dephasing of the molecular transition arising from the interaction with dissipative systems is described by a stochastic modulation of the electronic transition frequency. It is shown that in the case when the two laser pulses are short compared with the correlation time of the frequency modulation and when the spectral linewidth of the pump-laser light is smaller than the bandwidth of the equilibrium absorption spectrum, hole burning appears although the molecules have equal mean transition frequencies. This effect arises from non-Markovian correlations between the dephasings of the molecule during the actions of the pump- and the test-laser pulse. With increasing delay time the holes are smoothed out and disappear when the delay time exceeds the correlation time. Such effects were found in recent femtosecond absorption experiments by Shank et al. [in Ultrafast Phenomena V, dited by G. R. Fleming and A. E. Siegman (Springer, Berlin, 1986), p. 179].
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.
A general formula of the time-resolved optical spectrum for transient resonant light scattering is derived systematically by means of the operator algebra within the formalism of nonequilibrium thermo field dynamics (NETFD). The formula is applied to an analytically solvable model of the localized electron and phonon system, i.e., second-order light scattering due to the optically active three electronic states whose intermediate state is dynamically modulated by the phonon interaction mode. The derivation of the analytical expression for a four-point function, needed to obtain the spectrum, is performed with the help of the algebraic manipulations in NETFD, which showed the advantage of its methodology with respect to nonequilibrium transient phenomena. The three-dimensional profiles of the Raman and luminescence components in the time-resolved spectrum in the model are presented to show how the stochastic character comes out in the fast modulation limit, and how the dynamical behavior of the phonon system causing the modulation of the intermediate electronic state comes out in the slow modulation limit.