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Physical Review A

Influence of correlated stochastic perturbations on the nonlinear optical properties of a dimer

A.S. Cordan, Alex Boeglin, A. A. Villaeys

Published Aug 1, 1994• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.50.1664

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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.
The effect of stochastic laser phase fluctuations on nonlinear optical phenomena are investigated within the phase-diffusion model. Averaged equations of motion are derived in the limit of infinitely short correlation times and the results are applied to multiphoton absorption and to four-wave mixing. The effect of the stochastic phase fluctuations is shown to be equivalent to a T2{T}_{2}T2​ dephasing process, and a procedure is described for the inclusion of this equivalence in many nonlinear-optical problems. When a given mode contributes n photons to a multiphoton absorption process, its contribution to the width of the multiphoton transition is n2{n}^{2}n2 times its own stochastic width. When correlated lasers are used as the excitation sources in four-wave-mixing experiments, (new) stochastic-fluctuation-induced extra resonances in four-wave mixing (SFIER4) will be observed, in complete analogy to the extra resonances induced by collisions [pressure-induced extra resonances in form-wave mixing (PIER4)].
The nonlinear optical susceptibilities are analyzed in their optical propagation length considering the incoherent-coherent contributions with the dependence on the relaxation times. In addition, some symmetry properties of the Four-Wave mixing (FWM) signal concerning the frequency detuning exchange are used in the study, without restricting ourselves to the maxima of population oscillations. We analyze the behaviors of these optical responses in a vibronic coupling scheme using a molecule model consisting of two coupled harmonic curves of electronic energies with displaced minima in position and nuclear energies. The solvent effect in our model is treated through the natural Bohr frequency shift to a time-dependent function, with explicit manifestations in its comparison as if the upper state were broadened. Our results for both FWM signal propagation and nonlinear optical susceptibilities are sensitive to the intramolecular coupling parameters, solvent stochasticity, and perturbation order for the treatment of the weak probe beam. The consideration of a second-order probe beam in FWM would not represent a significant contribution to the predicted results, since its percentage contribution is negligible within the model development framework; however, this contribution becomes important when increasing the ratio between longitudinal and transverse relaxation times.
We investigate nonlinear wave mixing in two-level atoms wherein, using a dressed state formalism, it is shown that the signal arises as a consequence of quantum interference between relevant probability amplitudes for photon emission. We then report a theoretical study of the modifications that are induced in the four-wave mixing signals when the transition frequency of the atoms is stochastically modulated. Such modulations, which arise from perturbations in the immediate environment of the atoms, are shown to cause significant alterations in the nonlinear response of the atoms. We also describe how one can, via an investigation of the four-wave mixing signal, differentiate between Markov and non-Markov fluctuations in the transition frequency of the two-level system. The calculations rely on a recently developed Monte Carlo procedure that can be used to obtain exact solutions to a wide variety of spectroscopic problems, with minimal restrictions on atom, field, and noise parameters.
The nonlinear optical properties are studied theoretically of a molecular system immersed in a thermal bath and interacting with a four-wave mixing signal. A methodology based on cumulant expansions to obtain the average in the Fourier components associated with the coherences and populations, calculated by the optical stochastic Bloch equations, is employed. The system properties are analyzed as a function of the frequency detuning of the high-intensity pump beam and parameterized by the frequency detuning of the probe beam, both with respect to the Bohr frequency of the system. The longitudinal and transversal relaxation times and the bath effects, modeled as white noise, are also included as parameters in the calculation. Different cases, with degenerate and non-degenerate optical frequencies are examined and compared, resulting in differences related to the maximum in the population pulsation effects.