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We address theoretically the question of classical stochastic fieldsmimicking quantum states of light in the context of nonlinear spectroscopy andnonlinear optics, in particular two-photon absorption (TPA) and sum-frequencygeneration (SFG) driven by weak or bright broadband squeezed vacuum withtime-frequency entanglement between photons. Upon using a well-defined but adhoc subtraction of vacuum-energy terms (renormalization), we find that theclassical stochastic model yields exactly the same predictions as the fullquantum-field theory for all of the phenomena considered here, in both thelow-gain and high-gain regimes of squeezed vacuum. Such predictions include thelinear-flux scaling of TPA and SFG rates at low incident photon flux, as wellas the dependence of TPA and SHG rates on the relative linewidths of thesqueezed light and the ground-to-final-state transition in the material system,and the spectrum of SFG generated by bright squeezed vacuum.

Classical Model for Broadband Squeezed Vacuum Driving Two-Photon Absorption or Sum Frequency Generation