Quantum interference and quantum correlation, as two main features of quantum
optics, play an essential role in quantum information applications, such as
multi-particle quantum walk and boson sampling. While many experimental
demonstrations have been done in one-dimensional waveguide arrays, it remains
unexplored in higher dimensions due to tight requirement of manipulating and
detecting photons in large-scale. Here, we experimentally observe non-classical
correlation of two identical photons in a fully coupled two-dimensional
structure, i.e. photonic lattice manufactured by three-dimensional femtosecond
laser writing. Photon interference consists of 36 Hong-Ou-Mandel interference
and 9 bunching. The overlap between measured and simulated distribution is up
to 0.890±0.001. Clear photon correlation is observed in the two-dimensional
photonic lattice. Combining with controllably engineered disorder, our results
open new perspectives towards large-scale implementation of quantum simulation
on integrated photonic chips.Comment: 10 pages, 5 figure