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Europhysics Letters (EPL)

Transport and correlated fluctuations in the nonlinear optical response of excitons

Darius Abramavičius, Leonas Valkūnas, Shaul Mukamel

Published Sep 7, 2007• 49 citations
Publisher

Abstract

Closed expressions are derived for the femtosecond four-wave mixing of excitons which include slow Gaussian diagonal fluctuations (spectral diffusion) through the cumulant expansion and incoherent exciton transport induced by fast Markovian fluctuations. The interplay of both processes in the two-dimensional photon echo is demonstrated using model calculations for a dimer.

DOI
10.1209/0295-5075/80/17005

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Closed expressions are derived for the femtosecond four-wave mixing of excitons which include slow Gaussian diagonal fluctuations (spectral diffusion) through the cumulant expansion and incoherent exciton transport induced by fast Markovian fluctuations. The interplay of both processes in the two-dimensional photon echo is demonstrated using model calculations for a dimer.
Signatures of chemical exchange and spectral diffusion in 2D photon-echo line shapes of molecular aggregates are studied using model calculations for a dimer whose Hamiltonian parameters are stochastically modulated. Cross peaks induced by chemical exchange and by exciton transport have different dynamics and distinguish two models which have the same absorption spectrum (a two-state jump bath modulation model of a dimer and a four-state jump bath model of a single chromophore). Slow Gaussian-Markovian spectral diffusion of a symmetric dimer induces new peaks which are damped as the dipole moment is equilibrated. These effects require an explicit treatment of the bath and may not be described by lower-level theories such as the Redfield equations, which eliminate the bath.
The problem of correlated diagonal fluctuations is treated in the particular case of a dimer. Specifically, we analyze the influence of the correlation existing between the fluctuations on different sites. The local fluctuations induce a frequency modulation on the individual monomers. When these fluctuations are correlated, the internal dynamics of the dimer is altered. As a consequence, these intersite correlations give an additional contribution to the linear and nonlinear optical responses of the dimer. While this process has been discussed previously for \ensuremath{\delta}-function-correlated Gaussian-Markovian processes, we consider here the non-\ensuremath{\delta}-function-correlated case. The linear absorption spectrum and the third-order susceptibility in a degenerate-four-wave-mixing experiment are considered in order to emphasize the role of the correlated fluctuations in the linear and nonlinear regimes, respectively.
Three-pulse four-wave mixing is used to observe the loss of system memory for excitons confined in quantum wells. By measuring the photon echo peak shift with pulse delay, we obtain the two-time exciton frequency fluctuation correlation function. Spectral diffusion of localized excitons gives rise to exponential decay of the correlation function, while static inhomogeneity gives an offset. Nonmonotonic behavior during the first few picoseconds indicates complex memory effects due to the interaction of excitons with acoustic phonons.