Figure 1

(a) In Franson's proposal [4], a narrow-band laser photon produces a pair of energy-time entangled photons via spontaneous parametric down-conversion (SPDC). Each photon passes through different media characterized by second-order dispersion coefficient $\beta$. Fast photon counters register the photon pairs and allow to determine the average time difference in detection $\langle \Delta \tau \rangle$. For perfectly energy-time entangled photons with ${\beta }_2=-{\beta }_1$, the effect of the dispersions cancel, and the pairs exhibit no additional broadening. (b) In O’Donnell's experiment [17], the photon counters and coincidence detection are replaced by second-harmonic generation, which allows to probe dispersion effects on the fs time scale. (c) In the present work, we use a pair of classical laser pulses instead of entangled photons. We use second-harmonic generation, as in (b), but add narrow spectral filtering before detection of the second harmonic light. The detected light has the same temporal characteristics of that in (b), including dispersion cancellation.Reuse & Permissions

Figure 2

Experimental setup. The pulsed laser light from the Ti:sapphire is sent through a 4-F pulse shaper consisting of two 1200 l/mm gratings, two curved mirrors, and a 640-pixel spatial light modulator (SLM). Subsequently, the beams are separated into two arms by a 50:50 beam splitter (BS). In our experiment, positive dispersion in the sample arm (mode 1) can be introduced using two pieces of BK7 glass ($19.33\pm 0.03\text{mm}$ each), while the reference arm features an adjustable path delay $\tau$. To observe dispersion cancellation, the beams are focused by a 75-mm achromatic lens onto a 2-mm BiBO nonlinear crystal and the up-converted light is spectrally filtered by a grating and a slit before detection by a PMT.Reuse & Permissions

Figure 3

Experimental data. The normalized intensity of the up-converted light is shown as a function of the temporal delay $\Delta \tau$. (a) shows the dispersion-free case with a nearly Fourier-limited signal width ($21.7$ fs). This is in stark contrast to the cases where dispersion of (b) $\beta =850$ fs${}^2$ is added to arm 1 or (c) $\beta =-850$ fs${}^2$ is added to arm 2, where the signals broaden significantly to 172.7 and 176.4 fs, respectively. However, adding positive dispersion of $\beta =850$ fs${}^2$ to arm 1 and negative dispersion $\beta =-850$ fs${}^2$ to arm 2 yields the signal shown in (d), with a measured width of $21.9$ fs. In this last case, we show the dispersion is canceled in direct analogy with the quantum effect.Reuse & Permissions