Interference between distinguishable photons

Abstract: Two-photon interference (TPI) lies at the heart of photonic quantum technologies. TPI is generally regarded as quantum interference stemming from the indistinguishability of identical photons, hence a common intuition prevails that TPI would disappear if photons are distinguishable. Here we disprove this perspective and uncover the essence of TPI. We report the first demonstration of TPI between distinguishable photons with their frequency separation up to $10^4$ times larger than their linewidths. We perform time-resolved TPI between an independent laser and single photons with ultralong coherence time ($>10\ \mu$s). We observe a maximum TPI visibility of $72\%\pm 2\%$ well above the $50\%$ classical limit indicating the quantum feature, and simultaneously a broad visibility background and a classical beat visibility of less than $50\%$ reflecting the classical feature. These visibilities are independent of the photon frequency separation and show no difference between distinguishable and indistinguishable photons. Based on a general wave superposition model, we derive the cross-correlation functions which fully reproduce and explain the experiments. Our results reveal that TPI as the fourth-order interference arises from the second-order interference of two photons within the mutual coherence time and TPI is not linked to the photon indistinguishability. This work provides new insights into the nature of TPI with great implications in both quantum optics and photonic quantum technologies.