The intensity-amplitude correlation functions for a driven cavity QED system with two non-identical atoms are investigated in this paper. With the support of conditional homodyne detection, one can detect the time-dependent intensity-amplitude correlation functions experimentally. We find time-asymmetry in this correlation when the driving field is tuned to be resonant with the two-photon excitation state, which brings non-Gaussian fluctuations. The physical origin of these phenomena is the distinction of the third-order moment based on complete-collapse and partial-collapse, which corresponds to the measuring sequence of the intensity and amplitude. Finally, we also examined the nonclassical features of the system, which always exhibits photon bunching. The squeezing occurs in the region of weak driving and disappears with the increase of driving strength. Hence, a new classical inequality based on the technique of homodyne cross-correlation measurement is introduced to determine the nonclassicality of the non-Gaussian system in the region of unsqueezing.

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Frequency-resolved photon statistics of resonance fluorescence generated from a two-level system driven by a strong laser field and a weak laser field with equal frequencies are studied. The frequency resolution of fluorescent radiation is described by quantum filtering dynamics, which is simulated theoretically by two single-mode quantum optical cavities with tunable frequencies to scan the incident fluorescent radiation. By calculating the two-photon intensity-intensity correlation functions in terms of the cavity modes, we demonstrate that two-color strong correlations of resonance fluorescence can be generated not only between the opposite sidebands, but also between the central band and one of the sidebands, although both sidebands are broadened due to the perturbation of the weak laser field on the strong-field dressed atom. We emphasize that these properties are in contrast to the conventional case of standard single-atom Mollow triplet. Moreover, if the resonance frequencies of the two filtering cavities are tuned appropriately, broadband two-color strong correlations are predicted, and the physical origin is revealed from the perspective of quantum interference of photon emission dynamics. This can be considered as a feasible scheme for the design of broadband non-classical light sources, and may be beneficial to the quantum precise detection of atomic and molecular dynamics via quantum optical spectroscopy