## The interfering pathways that create the gated signal (21): (a) pathways responsible for the first term in equation (21)

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**Figure 2.** The interfering pathways that create the gated signal (21): (a) pathways responsible for the first term in equation (21). When the twin photons in beams 1 and 2 are indistinguishable, the two diagrams interfere destructively for δ*t* = 0, creating the HOM-dip in the photon correlation signal. (b) The pathways corresponding to the second term in equation (21). This interference also depends on the indistinguishability of the two beams, but in this case both photons can come from either of the two beams. The third term in equation (21) is not an interference term, and is not depicted.

**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.