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The Journal of Chemical Physics

Three-pulse photon echoes for model reactive systems

Mino Yang, Kaoru Ohta, Graham R. Fleming

Published Jun 1, 1999• 47 citations
Publisher

Abstract

A theoretical description of the three-pulse photon echo peak shift for model reaction systems is presented. An electronic two-state system with a finite upper-state lifetime and a three-state system in which electronic transitions can occur are considered. A probabilistic argument is employed to incorporate the incoherent transitions. New pathways describing the transition of electronic population are introduced and the nuclear propagator in the electronic population state is written by a convolution integral between those of the nonreactive two-state system weighted by some factors for the electronic transition. The response functions are given by multitime correlation functions and are analyzed by the cumulant expansion method. Some numerical calculations are presented and the influence of incoherent reactions on the peak shift is discussed. Comparison with experimental data confirms the existence of the effects predicted here.

DOI
10.1063/1.478957

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A theoretical description of the three-pulse photon echo peak shift for model reaction systems is presented. An electronic two-state system with a finite upper-state lifetime and a three-state system in which electronic transitions can occur are considered. A probabilistic argument is employed to incorporate the incoherent transitions. New pathways describing the transition of electronic population are introduced and the nuclear propagator in the electronic population state is written by a convolution integral between those of the nonreactive two-state system weighted by some factors for the electronic transition. The response functions are given by multitime correlation functions and are analyzed by the cumulant expansion method. Some numerical calculations are presented and the influence of incoherent reactions on the peak shift is discussed. Comparison with experimental data confirms the existence of the effects predicted here.
The third-order nonlinear optical response of energy transfer systems is theoretically investigated. A system composed of two chromophores having the same electronic transition energies is considered. The dynamics of energy transfer between the two chromophores is assumed to occur via a hopping (incoherent) mechanism. We introduce new types of pathways incorporating the hopping processes occurring while the system is in population states and reconstruct a third-order response function which is computationally viable. The nuclear propagators in the electronic population states are written as convolution integrals between those of the nonreactive two-state system weighted by some factors for the energy transfer. The response function is given by multitime correlation functions and these are analyzed by the cumulant expansion method. Based on this approach, the three-pulse photon echo peak shift for several models of energy transfer systems is discussed. It is shown that the rephasing capability of the induced signal is reduced by the memory loss due to resonant energy transfer. A previous model which incorporates resonant energy transfers in an intuitive way is reviewed and modified to supplement the loss of dynamic correlation of nuclear motion within the framework of the theory. The response function obtained by our new approach gives a more accurate description than the existing theory and a comparative discussion is given. The effect of inhomogeneity in rate constants on the third-order signal is discussed and the temperature dependence of the echo signal is examined.
A theoretical description of one- and two-color photon echo peak shifts (PEPS) and two-dimensional (2D) photon echo spectrum (PES) of a coupled chromophore system are presented. The effects of population relaxation in the one-exciton states on both the PEPS and the 2D PES are investigated. For values of time T shorter than the population relaxation time, a finite two-color peak shift magnitude and nonzero cross peaks in the 2D PES provide evidence of electronic coupling between the chromophores. These two distinct observables, i.e., PEPS and off-diagonal peaks, both originate from the electronic coupling. However, it is shown that the PEPS and 2D PES methods can provide complementary information on the structure-dependent nonlinear optical responses of coupled chromophore systems.
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Two-color three pulse photon echo peak shift spectroscopy (2C3PEPS) has been used to probe correlation in electronic transitions in two different regions of the electronic spectrum of a chromophore in the condensed phase. The 2C3PEPS can be done in an “uphill” or a “downhill” sense, where the first two interactions are of lower (higher) frequency than the final interaction with the radiation field. In both cases no correlation between the two spectral regions is observed at very short times. Different parts of the spectrum gain correlation owing to ultrafast solvent motion and the accompanying Stokes shift. We propose a model for the spectral shift that incorporates a conditional probability distribution for transition frequencies in the two spectral regions. The model qualitatively reproduces all the features of complete numerical simulations. Our results show that memory is partially conserved during the spectral diffusion process from the pump to the probe region. The downhill difference peak shift is very sensitive to the time scale of the inertial component of solvation and seems very promising for an accurate determination of this time scale.
The three-pulse photon echo technique has provided significant insight into ultrafast dynamics in a variety of condensed phase systems1. Clear signatures of non-Markovian dynamics in a dense potassium vapor2 provide the opportunity to gain further insight into the correlation function of frequency fluctuations both experimentally and theoretically. Here, experimental three-pulse photon echo peak shifts are compared to calculated peak shifts that include the long-range resonant interactions in a dense atomic vapor within an exciton formalism3. A slow exponential decay in the peak shifts is attributed to long-range resonant interactions.
A two-color photon echo peak shift measurement to probe the electronic coupling strength in molecular complexes is proposed. Exciton transfer between the electronic eigenstates is neglected and the baths associated with each monomer are assumed to be independent of each other. Within this simplified model, we derive a useful relation which can be used to estimate the electronic coupling strength via a combination of a normal one-color and the present two-color peak shift measurements. A simulation based on the cumulant expansion technique illustrates the validity of our suggestion.