Experimental Construction of NOON State Dynamics in Photonic Flat Band Lattices

We investigate the transport of path-entangled multi-photon NOON states in a flat-band photonic rhombic lattice and observe intriguing localization-delocalization features that depend on the phase as well as the photon number of the NOON states. To experimentally emulate photon number correlations, we develop an intensity correlation measurement protocol using coherent laser light with tunable relative phases. We first apply this protocol to show spatial bunching and anti-bunching of two-photon NOON states in a one-dimensional lattice consisting of identical waveguides. In the case of the rhombic lattice, we show that for an even (odd) photon number $N$, localization occurs at $0 \, (π)$ phase of the NOON state with a probability of $2^{1-N}$. Our results open an exciting route toward predicting quantum interference of correlated photons in complex photonic networks.