Time-Resolved Up-Conversion of Entangled Photon Pairs

In the process of spontaneous parametric down-conversion, photons from a pump field are converted to signal and idler photon pairs in a nonlinear crystal. The reversed process, or up-conversion of these pairs back to single photons in a second crystal, is also possible. Here, we present experimental measurements of the up-conversion rate with a controlled time delay introduced between the signal and idler photons. As a function of delay, this rate presents a full width at half maximum of 27.9 fs under our experimental conditions, and we further demonstrate that group delay dispersion of the photon pairs broadens this width. These observations are in close agreement with our calculations, thus demonstrating an ultrafast, nonclassical correlation between the signal and idler waves.

Figure 1

Experimental apparatus. Parametric down-conversion from lithium niobate crystal LN1 is collimated and sent through a series of 4 Brewster prisms, to be up-converted in a similar crystal LN2. Two mirrors (one fixed, the other on a piezoelectric stage, translated as shown) introduce a time difference $\tau$ between the upper and lower optical paths.

Figure 2

Experimental results. (a) Up-conversion rate $R(\tau )$ versus signal-idler delay $\tau$ for optimum dispersion. (b) $R(\tau )$ with up-conversion crystal $20°\mathrm{C}$ above phase-matching temperature. Other results are for additional signal-idler paths in 6 mm of fused silica [(c), solid curve], 12 mm of fused silica [(c), dot-dashed curve], and 37 mm of SF10 glass (d), showing increasing broadening of $R(\tau )$. Data in (c),(d) have been scaled to correct for Fresnel window losses.

Figure 3

Theoretical results. (a) Up-conversion rate $R(\tau )$ (arbitrary units) versus signal-idler delay $\tau$ for optimum dispersion. Also shown is $R(\tau )$ for additional common signal-idler dispersion due to 6 mm of fused silica [(b), solid curve, ${\varphi }^{\prime \prime }=99{\mathrm{fs}}^2$], 12 mm of fused silica [(b), dot-dashed curve, ${\varphi }^{\prime \prime }=198{\mathrm{fs}}^2$], 5 mm of SF10 glass [(c), ${\varphi }^{\prime \prime }=513{\mathrm{fs}}^2$] , and 37 mm of SF10 glass [(d), ${\varphi }^{\prime \prime }=3790{\mathrm{fs}}^2$].