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Photonics provide an efficient way to implement quantum walks, the quantumanalogue of classical random walk that demonstrates rich physics with potentialapplications. However, most photonic quantum walks do not involve photoninteractions, which limits their potential to explore strongly-correlatedmany-body physics of light. We propose a strongly interacting discrete-timephotonic quantum walk using a network of single atom beamsplitters. Wecalculate output statistics of the quantum walk for the case of two photons,which reveals the strongly-correlated transport of photons. Particularly, thewalk can exhibit either boson-like or fermion-like statistics which is tunableby post-selecting the two-photon detection time interval. Also, the walk cansort different types of two-photon bound states into distinct pairs of outputports under certain conditions. These unique phenomena show that our quantumwalk is an intriguing platform to explore strongly-correlated quantum many-bodystates of light. Finally, we propose an experimental realization based ontime-multiplexed synthetic dimensions.

A strongly interacting photonic quantum walk using single atom beam splitters