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The Journal of Chemical Physics

Probing the strength of the system-bath interaction by three-pulse photon echoes

Niklas Christensson, Benjamin Dietzek, Arkady P. Yartsev, Tõnu Pullerits

Published Jan 14, 2009• 10 citations
Publisher

Abstract

We explore how the width of the three-pulse photon echo signal at long population times can be used to determine the strength of the system-bath interaction. Using simulation with finite pulses we show that a simple relation exist between the width of the echo signal, the coupling strength, and the pulse autocorrelation. The derived model is applied to Rhodamine 6G in alcoholic solution, a paradigm system for the study of solvation dynamics, and the results are compared to conventional methods. The independently determined coupling strength forms the basis for a computationally inexpensive route to determine the entire spectral density, the key parameter when considering system-bath interactions. Our method allows us to accurately estimate the relative amplitude of fast and slow components in the correlation function using only impulsive limit simulations. We show that the peak shift significantly overestimates the amplitude of the fastest decay component for our experimental data. Changing solvent from methanol to 1-hexanol we observe a narrowing of the width of the echo profile. The changes in the echo width allow us to estimate the changes of the coupling strength in various solvents.

DOI
10.1063/1.2990652

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The Journal of Chemical Physics•Mar 8, 1995•138 citations
We explore how the width of the three-pulse photon echo signal at long population times can be used to determine the strength of the system-bath interaction. Using simulation with finite pulses we show that a simple relation exist between the width of the echo signal, the coupling strength, and the pulse autocorrelation. The derived model is applied to Rhodamine 6G in alcoholic solution, a paradigm system for the study of solvation dynamics, and the results are compared to conventional methods. The independently determined coupling strength forms the basis for a computationally inexpensive route to determine the entire spectral density, the key parameter when considering system-bath interactions. Our method allows us to accurately estimate the relative amplitude of fast and slow components in the correlation function using only impulsive limit simulations. We show that the peak shift significantly overestimates the amplitude of the fastest decay component for our experimental data. Changing solvent from methanol to 1-hexanol we observe a narrowing of the width of the echo profile. The changes in the echo width allow us to estimate the changes of the coupling strength in various solvents.
The decay of three-pulse photon echo signals from a solute in a liquid solvent is sensitive to the solute’s transition frequency fluctuations, as characterized by its two-point time correlation function, otherwise known as the solvation correlation function. The most widely used method for determining this solvation correlation function from photon echo data involves the three-pulse photon echo peak shift (3PEPS) method. Using this method the long-time decay of the solvation correlation function can be obtained directly, but the determination of the short-time decay requires a difficult numerical fitting procedure. In this study we propose several alternative approaches to determining the solvation correlation function from echo data, the most promising and straightforward of which we call the S3PE (short-time slope of the three-pulse photon echo) method. The accuracy and efficacy of this approach is illustrated by extracting the solvation correlation function from “experimental” data obtained from classical molecular dynamics computer simulations.
The time-integrated three-pulse photon echo is discussed in terms of the line-shape functions which are shown to be directly related to the solvation dynamics. By using the short-time approximation to the line-shape function, an algebraic form of the three-pulse photon echo signal S PE (τ, T ) is obtained as a function of two delay times, τ and T, between pulses. On the basis of the approximate form of the photon echo signal, the echo peak shift with respect to the second delay time (population evolution period) is derived and found to be linearly proportional to the time-dependent fluorescence Stokes shift function for times greater than the bath correlation time, τ c . In the case of intermediate inhomogeneous broadening, the asymptotic echo peak shift magnitude is found to be useful in estimating the static inhomogeneous width. To illustrate the theoretical results, an analysis of the echo peak shift measurement of IR144 in a room temperature glass, PMMA, is presented.
The influence of coupling strength and temperature on the solute–solvent interaction of two chromophores in polymer glass is reported. The three-pulse photon echo peak shift method was used to study the dye IR144 in polyvinylformal (PVF) and the dye DTTCI (3,3′-diethylthiatricarbocyanine iodide) in polymethylmethacrylate (PMMA). IR144 is more strongly coupled (larger reorganization energy) to both its intramolecular modes and to the solvent than is DTTCI. Our results can be well described by the linearly coupled harmonic bath model over the range 300 to 30 K. In particular, the strikingly different temperature sensitivities of the long-time (asymptotic) peak shift are well described by the theory. Temperature-independent spectral densities and inhomogeneous widths suffice to quantitatively describe the peak shift data over this temperature range and a number of numerical predictions based on the theoretical model are experimentally confirmed. An ultrafast component corresponding to a decay of ∼100 fs time scale in the transition frequency correlation function is found in all cases, though the amplitude is small for the DTTCI solutions. This ultrafast response is assigned to the inertial response of the solvent. The inertial response measured for DTTCI in PMMA is very similar to our previous measurements of the inertial response for IR144 in PMMA, suggesting that a general characteristic of the solvent is being probed. The weaker coupling of DTTCI produces a drastic increase in the width of the photon echo signal as predicted by theory and strong vibrational quantum beats at 30 K. By contrast, such beats are not observed in the echo signal for IR144.
Abstract This account summarizes our recent work on measurements of the correlation function of the transition frequency fluctuations by a three-pulse photon echo method. The correlation function of the transition frequency fluctuations is a sensitive measure for the magnitudes and time scales of dynamical interactions between solute and solvent. We describe the results of the solvation dynamics of small ions in protic solvents such as methanol and water obtained by an infrared photon echo method.
Two- and three-pulse photon echo signals are calculated for various model systems. The use of an experimental solvation correlation function as the solvent fluctuation correlation function leads to two conclusions. First, inertial solvent motion plays a major role in the electronic dephasing process. Second, simple models such as Markovian or exponential models for the solvent fluctuation correlation function may not provide an adequate description of the echo signal. The real and imaginary parts of the echo response, which may be measured via heterodyne detected stimulated photon echoes, are compared with conventional photon echo signals.
The connection between dephasing of optical coherence and the measured spectral density of the pure solvent is made through measurements and calculations of photon echo signals. 2-pulse photon echo measurements of a cyanine dye in polar solvents are presented. Signals are recorded for both phase matched directions enabling accurate determination of the echo signal time shift. Echo signals are calculated by two approaches that employ the response function description of nonlinear spectroscopy; (i) a single Brownian oscillator line shape model, and (ii) the line shape obtained using the solvent spectral density. The strongly overdamped Brownian oscillator model incorporates only a single adjustable parameter while the experimental data present two fitting constraints. The second model incorporates the measured solvent spectral density. Both give very good agreement with the experimental results. The significance of the second method lies in this being a new approach to calculate nonlinear spectroscopic signals, for comparison with experimental data, that uses directly the measured spectrum of equilibrium fluctuations of the solvent. This approach also provides a better conceptual perspective for deriving insight into the nature of the solute–solvent coupling mechanism. Comparing the parameters for the strength of interaction in a variety of polar solvents it is found that the coupling involves the solvent polarizability and not the solvent polarity. The interaction mechanism cannot be deduced from the Brownian oscillator calculations.