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Physical Review Letters

Influence of non-Markovian effects in degenerate four-wave-mixing processes

J. P. Lavoine, A. A. Villaeys

Published Nov 1, 1991• 9 citations
Publisher

Abstract

In this work, we analyze the influence of non-Markovian effects on a pulsed time-delayed four-wave-mixing experiment. By using a perturbative approach the density matrix equations are solved for a medium modeled by two-level systems and excited by short pulses. We show that the intensity of the diffracted light can be expressed as a simple function of the bath memory function. This demonstrates the interest of such an experiment to get information on the bath.

DOI
10.1103/physrevlett.67.2780

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The Journal of Chemical Physics•Sep 7, 2007•11 citations
In this work, we analyze the influence of non-Markovian effects on a pulsed time-delayed four-wave-mixing experiment. By using a perturbative approach the density matrix equations are solved for a medium modeled by two-level systems and excited by short pulses. We show that the intensity of the diffracted light can be expressed as a simple function of the bath memory function. This demonstrates the interest of such an experiment to get information on the bath.
The transient four-wave mixing signal from a three-level system coupled to a bath of harmonic oscillators is calculated in the short-pulse limit. This allows an examination of the non-Markovian effects on the relaxation processes in the excited levels between which beating occurs. In particular, it is possible to distinguish between oscillations which are due to oscillatory dephasing, a consequence of the memory effects, and oscillations due to the quantum beats. This also allows one to analyze how these two kinds of oscillations are mixed together. We show that we not only have an amplitude modulation of the beats as in the Markovian case but also deformations of the beats for short delays between the exciting light pulses. These deformations are a consequence of the nonequilibrium motion of the surroundings of the system under optical excitation. \textcopyright{} 1996 The American Physical Society.
We present a time-resolved study of the diffracted pulse in degenerate four-wave mixing experiments with short-response-time materials. The first step is the validation of a theoretical model that takes into account the temporal characteristics of the energy level (relaxation time T1 and dephasing time T2) and of the incident pulse (duration and spectral phase) in a simple particular case. Two methods are used for characterizing the diffracted beam: the amplitude correlation with the reference pulse and the spectrum intensity measurements. We discuss the experimental results, which show good agreement with the theoretical model and evidence the strong influence of the incident pulse characteristics.
The main goal of this paper is to analyze a two-photon degenerate four-wave-mixing process that occurs in an isotropic media modeled by homogeneously broadened two-level systems having unequal permanent dipole moments and subject to rotational diffusion. Our theoretical treatment is based upon a third-order perturbative solution of the density-matrix equations and does not require the rotating-wave approximation. The medium being excited by three stationary fields, we give an analytical expression of the macroscopic polarization up to the third order, including permanent dipole moments, orientational diffusion, and field polarizations. We apply these general results to the description of a degenerate four-wave-mixing process by selecting, in the expressions, the contributions in the direction ${\mathbf{k}}_{\mathrm{\ensuremath{\alpha}}}$-${\mathbf{k}}_{\mathrm{\ensuremath{\beta}}}$+${\mathbf{k}}_{\ensuremath{\gamma}}$, ${\mathbf{k}}_{\mathrm{\ensuremath{\alpha}}}$, ${\mathbf{k}}_{\mathrm{\ensuremath{\beta}}}$, and ${\mathbf{k}}_{\ensuremath{\gamma}}$ being, respectively, the wave vectors of the exciting fields. We show that the two-photon degenerate four-wave mixing is dependent on the permanent dipole moments and is not present if these dipole moments are equal or zero. We analyze the influence of rotational diffusion. Different cases of field polarizations are also considered, and we discuss a comparison of the well-known one-photon degenerate four-wave-mixing process and this two-photon process. This process is also discussed in the particular case of phase conjugation.
Oscillatory dephasing is a characteristic of non-Markovian relaxation phenomena when the coherence losses are essentially due to pure dephasing processes. In this paper, we wish to consider the case where the phase relaxation is essentially due to population decay. To this end, we calculate the transient four-wave mixing signal in the short pulse limit from a three-level sytem nondiagonally coupled to a bath of harmonic oscillators. We will show that no oscillatory dephasing is observed in the non-Markovian regime, only a nonexponential decay. Therefore, oscillatory dephasing appears to be a signature of pure dephasing processes.
A two-pulse degenerate four-wave mixing experiment is analyzed in the case where the medium under investigation can be modeled by two-level systems having unequal permanent dipole moments. By modeling the light pulses by double exponentials [exp(-Gamma/t/)], we give an analytical expression of the third-order nonlinear polarization of the medium. We apply this result to simulate the measured signal in such experiment. We show that in the case of a two-photon transition, a signal can be detected if the pump pulse interacts with the medium before the probe pulse contrary to what is observed for excitations in the resonance region. An attempt to explain this behavior is made and the detected signal is analyzed in terms of pure coherent processes. This effect appears as a signature of the presence of permanent dipole moments. To test this property on a more realistic system, we then have considered a one-dimensional frequency-selected infrared degenerate four-wave mixing experiment on a molecular anharmonic vibrational mode modeled by a Morse potential and coupled to a dissipative bath of harmonic oscillators. We show that the two-photon transitions allowed by the presence of permanent dipole moments enable to analyze the multilevel system dynamics as if they were the one of a two-level system. Our results can also be extended to the case of inhomogeneous broadening and are of interest to study the infrared photon-echo response of anharmonic vibrational modes.