## Equation (36) on resonance is plotted versus the pump intensity |α|^{2} with an off-resonant intermediate state at *e* = 12 500 cm^{−1}

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**Figure 7.** Equation (36) on resonance is plotted versus the pump intensity |α|^{2} with an off-resonant intermediate state at *e* = 12 500 cm^{−1}. The coherent (red) and the incoherent (blue) contributions are plotted separately. The dashed, grey line is the linear approximation of the coherent term. Inset: equation (36) versus the pump frequency ω_{p} for *T* = 100 fs, σ_{p} = 10 cm^{−1} and |α|^{2} = 0.001.

**Abstract**

Time- and frequency-gated two-photon counting is given by a four-time correlation function of the electric field. This reduces to two times with purely time gating. We calculate this function for entangled photon pulses generated by parametric down-conversion. At low intensity, the pulses consist of well-separated photon pairs, and crossover to squeezed light as the intensity is increased. This is illustrated by the two-photon absorption signal of a three-level model, which scales linearly for a weak pump intensity where both photons come from the same pair, and gradually becomes nonlinear as the intensity is increased. We find that the strong frequency correlations of entangled photon pairs persist even for higher photon numbers. This could help facilitate the application of these pulses to nonlinear spectroscopy, where these correlations can be used to manipulate congested signals.