Classical analog for dispersion cancellation of entangled photons with local detection

Energy-time entangled photon pairs remain tightly correlated in time when the photons are passed through equal magnitude, but opposite in sign, dispersion. A recent experimental demonstration has observed this effect on ultrafast time-scales using second-harmonic generation of the photon pairs. However, the experimental signature of this effect does not require energy-time entanglement. Here, we demonstrate a directly analogue to this effect in narrow-band second harmonic generation of a pair of classical laser pulses under similar conditions. Perfect cancellation is observed for fs pulses with dispersion as large as 850 fs$^2$, comparable to the quantum result, but with an $10^{13}$-fold improvement in signal brightness.