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Physical Review Letters

Time-Resolved Resonance Fluorescence and Resonance Raman Scattering

A. Szöke, E. Courtens

Published Apr 21, 1975• 32 citations
Publisher

Abstract

Light emission under near-resonant excitation by a pulsed optical field is described using a semiclassical (Bloch) model for the near-resonant transition. Adiabatic excitation of this transition leads to Raman emission, whereas nonadiabaticity gives fluorescence. The model describes quantitatively observed relaxation effects. It further predicts that such experiments can determine the power spectrum of the correlation function characterizing collisions, offering an alternative to off-resonance spectroscopy.

DOI
10.1103/physrevlett.34.1053

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Light emission under near-resonant excitation by a pulsed optical field is described using a semiclassical (Bloch) model for the near-resonant transition. Adiabatic excitation of this transition leads to Raman emission, whereas nonadiabaticity gives fluorescence. The model describes quantitatively observed relaxation effects. It further predicts that such experiments can determine the power spectrum of the correlation function characterizing collisions, offering an alternative to off-resonance spectroscopy.
The theory of resonance Raman effect, resonantly enhanced two-photon absorption, and resonance fluorescence---valid also for strong fields---is treated in a unified and simplified way. Dressed states, Bloch equations, and perturbation theory are used to calculate line positions, and integrated intensities both for steady state and transient excitation. The case of adiabatic following is solved explicitly; it occurs when an off-resonance incident pulse is turned on and off slowly. It leads to the identification of Raman scattering, two-photon absorption, and Rayleigh scattering with an adiabatic process while fluorescence and consecutive two-photon absorption with nonadiabaticity. Time-dependent spectra are defined in a rigorous way. Our formulas agree in the various limits with those that appear in the literature.
The review deals with various variants of classification of the types of secondary emission of light by molecules; cases are distinguished in which the secondary emission occurs without additional processes that find their way between photon emission and absorption; the advisability of differentiating between the cases of resonance fluorescence and resonance scattering is noted. Reference is made to papers that have made contributions to the development of quantum-mechanical and classical theory of Raman scattering and to the development of the concepts of the relations between electron-vibrational absorption spectra, fluorescence spectra, and scattering excitation near and near and far resonance. Conditions are considered of excitation of the spectrum at different relations between the electronic-oscillator damping constant, the atom vibration frequency, the rotational frequencies, and the difference between the frequency of the incident light and the frequency of the electronic transition. The conditions for the excitation of typical light scattering, typical resonance fluorescence, and certain intermediate types, in which individual features of scattering are combined with certain features of fluorescence (phenomena of the transition type) are noted. The results of investigations of different models of the scattering centers, their advantages, shortcomings, and limits of applicability are compared. The most interesting results of the experimental investigations of resonant scattering of light by molecules and crystals are noted.
Abstract Double resonance, resonance Raman and resonance fluorescence are discussed in terms of a superposition of adiabatic states. The adiabatic states are the instantaneous eigenstates of a two‐level Hamiltonian which includes the interaction with a near‐resonant coherent pulse and which has been transformed by a unitary transformation so that its only time‐dependence is that of the field envelope of the pulse. Resonance Raman results from spontaneous transitions to a third, lower state from the adiabatic following state which reduces to the initial (lower) state of the two‐level system in the absence of radiation. Resonance fluorescence is produced by spontaneous transition to the lower third state from the upper adiabatic state which reduces to the upper state of the two‐level system in the absence of radiation. Differential equations allowing the calculation of the probability amplitudes of the adiabatic states are given and a method of solving these equations by successive approximation is proposed. Saturation effects such as dynamic Stark shift and splitting (Autler—Townes effect) and optical nutation are interpreted in terms of perturbation of adiabatic energy levels and interference effects between adiabatic states. The possibility of observing optical nutation in a two‐level system by using time‐resolved double resonance experiments is suggested. Decay of the states of the two‐level system is taken into account leading to extended adiabaticity conditions which show that adiabatic following becomes possible even at resonance. For weak fields it is shown that adiabatic following at resonance can produce light scattering narrower than the linewidth as predicted by Heitler. The adiabatic states theory has also been extended to near‐resonance multiphoton interaction for systems that can be described by an effective two‐level Hamiltonian.
Competitive behavior of two channels of resonant Raman scattering and luminescence is discussed for the giant two-photon excitation of excitonic molecules in CuCl. The stochastic theory of intermediate state interaction is applied to describe the time-integrated and time-resolved emission spectra of the excitonic molecule excited resonantly by a short light pulse. Particularly as for the time-resolved spectrum, the frequency-time uncertainty due to the finite observation time is incorporated in the present theory. Our theory explains the observed characteristics of the emission spectra, and the relaxation constants of the excitonic molecule and the exciton in the final state are determined from comparison between the observed and calculated spectra.
Based on the time-dependent theory, an analysis of the distinction between resonance Raman (RR) and resonance fluorescence (RF) with pulse excitation was presented. The real population of the intermediate state gives two optical components-the independent time evolution of intermediate ket and bra states generates RR while RF originates from the phase coherent between ket and bra states. In cw limit, the transition probability of spontaneous emission with pulse excitation can be reduced to the classical theory.
Time dependent description of resonance Raman scattering is performed for a general system, by a density matrix reformulation of damping theory originally used for resonance fluorescence of atom. Radiative damping in the intermediate states can be described in terms of "damping operator" in realistic situations. In large ergodic systems, the scattering reduces to luminescence if the relaxation time within the excited states is much shorter than the radiative lifetime. In a typical case, time resolved emission spectra consist of various stages (i) scattering complex where absorption and emission are inseparable, (ii) dynamical and then (iii) kinetic relaxations giving rise to the hot luminescence, which finally converges to (iv) the ordinary luminescence from relaxed excited states. Hot luminescence does not appear within a motionally narrowed line. The interpretation of spectra depends also on the method of observation.