We theoretically investigate the two-photon absorption signals of a three-band (g, e, f) system diagonally coupled to an over-damped Brownian oscillator bath, which induces random Gaussian modulations of energy levels with an arbitrary degree of correlation. For fast modulation, extra 2ωeg and 2ωfe peaks may obscure the g–f transitions in the classical two-photon absorption (CTPA) spectra for nearly resonant e states. These peaks arise from one-photon resonant g–e or e–f transitions. In the slow modulation limit, these peaks vanish because of the short tails of the Gaussian line shape. CTPA strongly depends on the correlations between energy fluctuations. In entangled two-photon absorption, the extra peaks are eliminated because of the broad one-photon but narrow two-photon spectrum of the twin photons. The variation of the coherences between f states with the correlation between energy fluctuations is explored.

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