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Laser Chemistry

Complete Determination ofRelaxation Parameters FromTwo‐Dimensional RamanSpectroscopy

Vladimir Chernyak, Andrei Piryatinski, Shaul Mukamel

Published Jan 1, 1999• 11 citations
Publisher

Abstract

Using the model of a weakly‐anharmonic, underdamped oscillator coupled to a bath, we demonstrate that the 2D time‐resolved Raman signal carries information about the population decay T1, the homogeneous dephasing T2, and the inhomogeneous dephasing T1 relaxation timescales. We distinguish between two projections of the 2D signal: first, the echo signal, which is stretched in the diagonal direction decays with T2, and the second which is stretched along one axis is related to the population relaxation and decays with T1. The width of both signals reflects T1. Equations of motion for vibrational coherence and population variables are employed in these calculations.

DOI
10.1155/1999/26946

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Using the model of a weakly‐anharmonic, underdamped oscillator coupled to a bath, we demonstrate that the 2D time‐resolved Raman signal carries information about the population decay T1, the homogeneous dephasing T2, and the inhomogeneous dephasing T1 relaxation timescales. We distinguish between two projections of the 2D signal: first, the echo signal, which is stretched in the diagonal direction decays with T2, and the second which is stretched along one axis is related to the population relaxation and decays with T1. The width of both signals reflects T1. Equations of motion for vibrational coherence and population variables are employed in these calculations.
We employ multi-level Redfield theory and the equation-of-motion phase-matching approach to model two-dimensional electronic photon-echo signals of a vibronic dimer weakly coupled to an uncorrelated harmonic bath. The vibronic manifold of the dimer is formed by Franck-Condon active vibrational modes (one mode per monomer). We study the effect of the coupled exciton-vibrational dynamics on the two-dimensional photon-echo profiles. Our main focus is the relationship of the system coherences to the oscillatory behavior of the cross-peak intensities with population time. The work represents the first step towards detailed understanding of oscillative signatures in two-dimensional electronic photon-echo signals of vibronic oligomers.
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A quantum-mechanical treatment of the dynamics of relaxation of a twolevel mode coupled to a thermal bath is presented. The Zwanzig-Mori projection-operator formalism is employed to derive exact equations of motion for the correlation function and the excess population , where and are the coordinate and number operators associated with the two-level mode. In the van Hove weak-coupling limit it is shown that |G ν|2 and Δn decay exponentially with time constants τ and τ′, respectively. Explicit expressions for τ and τ′ are determined and the relationship between them clearly established. The application of the model to the specific problem of the effects of vibrational relaxation on isotropic Raman spectral lineshapes in dense media is emphasized.
The coherence spike observed in the transmitted probe intensity decay curve in pump–probe experiments is analyzed with a model which depends explicitly upon the population decay and dephasing rate constants. Using this model and simple pulse shape functions a series of decay curves are calculated throughout the range of wide to narrow pulse widths relative to the dephasing time. These calculations suggest that the coherence spike may be used to obtain information about the phase coherence in the electronic or vibrational transition being investigated, when the pulse width is comparable to or smaller than the dephasing time. Methods of extracting T2 from the coherence spike are also discussed.
Two-dimensional (2D) line shapes derived from four types of coherent third-order nonlinear spectroscopies as a function of two independent time or frequency variables are compared. The signals scattered into two wave-vector-matching directions in the limits of high-time or high-frequency resolution are calculated for an inhomogeneously broadened ensemble of two-level systems with phenomenological dephasing and population relaxation times. While one-dimensional (1D) line shape analysis for this model is ambiguous, the contours of these 2D line shapes are shown to be characteristic of the relative time scales of the three relevant line-broadening parameters. These broadening mechanisms are also apparent by comparing 2D spectral profiles along the diagonal and antidiagonal frequency axes. For time domain experiments, in analogy with NMR correlation spectroscopy, the radiated signal is observed as a function of the two coherence periods and is 2D Fourier transformed to obtain a line shape. For experiments based on the photon echo, the ellipticity of the absolute value 2D line shape is related to the ratio of the inhomogeneous width to the dephasing rate, whereas experiments based on the transient grating method are shown to be functionally 1D. For frequency domain experiments, the contours of the 2D line shape can yield information on static and both dynamic broadening mechanisms. While the addition of spectral diffusion to such calculations will modify these results for frequency domain experiments, characterizing these dynamics in the time domain naturally leads to a 3D experiment analogous to the spin diffusion experiment in NMR.
A detailed theoretical analysis is presented of the dephasing signal measured in four-beam picosecond time-resolved stimulated-Raman-gain experiments. The analytical expressions derived are successful in simulating observations on the CS2 model system under various experimental conditions. It is established that the tail of the curve for sufficiently long delay times is uniquely determined by the vibrational Raman term that yields the vibrational dephasing time T2. It is also found that the rotational dephasing time cannot be fundamentally determined from the rotational Raman peak centered around zero delay. Furthermore, it is shown that the coherence properties of the stimulating laser fields, as distinguished from their pure pulse-envelope properties, are crucially important in determining the time resolution of the experiments and for explaining several experimental phenomena observed under mismatched excitation-pulse conditions. In this respect, the domain model for mode-locked pulses has proved to be useful. It is found that the time resolution of the dephasing measurements is determined by the combined pulse-coherence time of the driving fields and not by the cross-correlation width of the pulse envelopes.