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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Time-resolved optical spectrum for transient resonant light scattering

Toshihico Arimitsu, Naoko Arimitsu

Published Jul 1, 1994• 8 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.50.121

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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.
A general theory of transient light scattering is developed on the basis of our stochastic theory of intermediate state interaction. The transient behaviors of various components of the second order optical process under a pulsed irradiation are discussed and model calculations of the time-resolved emission spectra are performed. It is clarified that in the fast modulation limit the Raman component has a time constant determined by the phase memory time of the intermediate state while the time constant of the luminescence component is given by the radiative damping rate. The transient behaviors of the scattered light intensity are also discussed.
Raman spectroscopy uses light scattering to extract information on low-energy excitations of solids. The Raman process is described by diagrams which are fourth order in the light-matter interaction and in particular the resonant contribution, which involves four different space-time arguments, is difficult to evaluate. If one instead simulates explicitly the incoming (classical) light pulse, the Raman signal is given by the outgoing photon flux and can be determined from a two-point correlation function. Such a formalism can be used to compute the time-resolved Raman spectrum of nonequilibrium systems, as well as nonlinear signals which are higher order in the incoming field, such as hyper-Raman scattering. Here we explain how to implement this time-dependent formalism within the dynamical mean field theory framework. The method is illustrated with applications to the Holstein-Hubbard model in the strong electron-phonon coupling regime. We demonstrate hyper-Raman scattering in measurements with strong probe fields and frequency mixing signals in the presence of a pump field and simulate the evolution of Stokes and anti-Stokes features after photoexcitations of metallic and Mott insulating systems.
The quantum mechanical description of the transient resonance Raman scattering including both the excitation and observation processes is presented. To obtain the general formula for the actually observable transient emission spectrum, the following way of observation is proposed; the use of a spectroscope for wave transformation and a photon-counter behind it for particle transformation. On its basis, the transient emission spectrum and its average over the duration time of photon-counting are explicitly defined especially for systems small compared with the spacial extent of an incident pulse. It will be shown that the transient emission spectrum conforms to the minimal case of the Heisenberg uncertainty relation through the restriction for the emission time coming from the Fourier transform of the transfer function of the spectroscope. The theory is applied to a strongly coupled localized electron-phonon system. It will be shown that what aspects of the correlation between absorption and emission are disclosed depends strongly on both the ways of excitation and observation.
The stochastic theory of intermediate state interaction developed in a preceding paper is applied to more realistic models to discuss the correlation between the incident and the scattered photons in more detail. Through these model calculations it is confirmed that the spectral characteristics of the second order optical process are determined by a few physical parameters of the radiative damping rate and the modulation amplitude and rate. In the slow modulation limit the relative intensity ratio between the broad Raman component and the luminescence is almost determined by the ratio between the radiative damping rate (γ b ) and the modulation rate (γ m ). In the fast modulation limit the ratio between the δ-shaped Raman component if it exists and the luminescence is given by the ratio between γ b and the dephasing relaxation rate Δ 2 /γ m ( Δ denotes the modulation amplitude.).
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.
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.