Intensity Correlation Measurement to Simulate Two-body BICs and Probe Nonlinear Discrete Breathers

We study Hanbury Brown-Twiss spatial intensity correlations in femtosecond laser-fabricated photonic Su-Schrieffer-Heeger lattices using coherent input states with tunable phases. By mapping intensity correlations to the two-body quantum walk, we experimentally simulate edge bound states in the continuum (BICs) of two indistinguishable bosons. These two-body edge BICs show remarkable robustness in the presence of disorder. We then discuss how intensity correlations can capture the dynamics of two identical fermions for which BICs do not exist on the same edge of the lattice. The localization of intensity correlation, observed in the linear regime, persists at weak nonlinearity due to the formation of long-lived edge breathers -- spatially localized nonlinear states with oscillating intensity along the propagation distance. For stronger nonlinearities, localized edge states are not formed for a range of phases, destroying the localization of the intensity correlation. Our results highlight the interplay of band structure, initial state, and nonlinearity influencing transport and intensity correlations.