Theory of Two-Photon Absorption with Broadband Bright Squeezed Vacuum: Part 1 Quantum Model

We present an analytical quantum theoretic model for molecular two-photon absorption (TPA) of broadband, spectrally multi-mode squeezed vacuum with pulse duration much greater than the coherence time, including low-gain (isolated entangled photon pairs or EPP) and high-gain (bright squeezed vacuum or BSV) regimes. We treat only cases where the exciting light is spatially single-mode and is nonresonant with all intermediate molecular states. In the case of high gain, we find that if the linewidth of the final molecular state is much narrower than the bandwidth of the exciting light, bright squeezed vacuum is found to be equally (but no more) effective in driving TPA as is a quasi-monochromatic coherent-state (classical) pulse of the same temporal shape, duration and mean photon number. Therefore, the sought-for advantage of observing TPA at extremely low optical flux is not provided by broadband bright squeezed vacuum. In the opposite case that the final-state linewidth is much broader than the bandwidth of the BSV exciting light, we show that the TPA rate is proportional to the secondorder intensity autocorrelation function at zero time delay , as expected. And we find that for to reach the idealized form , with being the mean number of photons per temporal mode, it is required to compensate the dispersion inherent in the nonlinearoptical crystal used to generate the BSV. Part 2 of this two-paper series considers the same questions in the context of a classical model of squeezed light and also extends the analysis to the case of sum-frequency generation.