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Physical Chemistry Chemical Physics

Appearance of intramolecular high-frequency vibrations in two-dimensional, time-integrated three-pulse photon echo data

Benjamin Dietzek, Niklas Christensson, Pär Kjellberg, Torbjörn Pascher, Tõnu Pullerits, Arkady P. Yartsev

Published Dec 15, 2006• 22 citations
Publisher

Abstract

An alternative experimental outline to measure homodyne detected three-pulse photon-echo data is presented. The novel experimental approach allowing for online monitoring and correction of experimental timing and stability is discussed in detail using the paradigm system of Nile blue in alcohol solution. It is shown that excellent signal-to-noise ratios together with high reproducibility of the data can be routinely achieved. We report in detail on the appearance of high-frequency intramolecular vibrations in the two-dimensional three-pulse photon-echo data and suggest that besides the conventionally discussed three-pulse photon-echo peak-shift the width of the integrated echo signal as a function of population time contains identical and easily accessible information on high-frequency intramolecular vibrations. A comparison of experimental data with theoretical modeling is performed showing that the observed echo-width oscillations are in line with predictions of the Brownian oscillator model.

DOI
10.1039/b614332f

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An alternative experimental outline to measure homodyne detected three-pulse photon-echo data is presented. The novel experimental approach allowing for online monitoring and correction of experimental timing and stability is discussed in detail using the paradigm system of Nile blue in alcohol solution. It is shown that excellent signal-to-noise ratios together with high reproducibility of the data can be routinely achieved. We report in detail on the appearance of high-frequency intramolecular vibrations in the two-dimensional three-pulse photon-echo data and suggest that besides the conventionally discussed three-pulse photon-echo peak-shift the width of the integrated echo signal as a function of population time contains identical and easily accessible information on high-frequency intramolecular vibrations. A comparison of experimental data with theoretical modeling is performed showing that the observed echo-width oscillations are in line with predictions of the Brownian oscillator model.
The integrated three-pulse photon echo signal of Nile blue doped in poly(methyl methacrylate) (PMMA) was measured two-dimensionally by varying the first coherence period and the subsequent population period. The electronic dephasing time was in the femtosecond time range even at low temperatures, whereas rephasing and echo formation were still possible even when the population period was extended to >100 ps. Oscillation was present in the echo signal even when population period was extended to longer values than the dephasing time of the vibrational coherence. Echo peak shift measurement indicated a presence of small spectral diffusion in the picosecond time range. A computer simulation was carried out from a model spectral density. The phonon mode of PMMA was represented by a Brownian oscillator centered at ∼116 cm -1, and it reproduced the temperature dependence of the echo signal surprisingly well.
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.
A theoretical analysis is carried out for the recently developed three-pulse photon echo spectroscopy employing dual frequency combs (DFC) as the light sources. In this method, the molecular sample interacts with three pulse trains derived from the DFC, and the generated third-order signal is displayed as a two-dimensional (2D) spectrum that depends on the waiting time introduced by employing the asynchronous optical sampling method. Through the analysis of the heterodyne-detected signal interferogram using a local oscillator derived from one of the optical frequency combs, we show that the 2D spectrum closely matches the spectrum expected from a conventional approach with four pulses derived from a single femtosecond laser pulse, and the waiting time between the second and third field-matter interactions is given by the down-converted detection time of the interferogram. The theoretical result is applied to a two-level model system with solvation effect described by solvatochromic spectral density. The model 2D spectrum reproduces spectral features such as the loss of frequency correlation, dephasing, and spectral shift as a function of the population time. We anticipate that the present theory will be the general framework for quantitative descriptions of DFC-based nonlinear optical spectroscopy.
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.