Based on three stochastic models, the subtle, Markovian field-correlation effects have been investigated in homodyne-detected attosecond sum-frequency Raman-enhanced polarization beating (REPB) and heterodyne-detected femtosecond difference-frequency REPB. The different roles of the amplitude fluctuations and the phase fluctuations have been pointed out in both time and frequency domains. Analytic closed forms of the sixth-order and fourth-order Markovian stochastic correlations are characterized for homodyne (quadratic) and heterodyne (linear) detection, respectively. The attosecond sum-frequency REPB signal shows resonant–nonresonant cross correlation, asymmetric temporal behavior, and drastic difference for three Markovian stochastic fields, and the autocorrelation of REPB exhibits hybrid-radiation-matter-detuning-terahertz damping oscillation. The phase-diffusion model predicts a damping oscillation of the signal around a constant value in the narrowband case. The heterodyne-detected signal of REPB potentially offers rich dynamic information about the homogeneous, broadening, material phase of the third-order nonlinear susceptibility.
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