## The four-point field correlation function in the frequency domain, langle E^{dagger } (omega ^{prime }_a) E^{dagger } (omega ^{prime }_b) E (omega _b = 11,000 ; { m cm}^{-1}) E (omega _a) angle, equation (A.13)

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**Figure 6.** The four-point field correlation function in the frequency domain, \langle E^{\dagger } (\omega ^{\prime }_a) E^{\dagger } (\omega ^{\prime }_b) E (\omega _b = 11\,000 \; {\rm cm}^{-1}) E (\omega _a) \rangle, equation (A.13). The pulse parameters are ω_{1} = ω_{2} = ω_{p}/2 = 11 000 cm^{−1}, σ_{p} = 50 cm^{−1} and *T* = 100 fs. The pump intensity is increased from left to right: (a) |α|^{2} = 0.000 05, (b) 0.0001, (c) 0.0005 and (d) 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.