Quantum correlations in integrated waveguide structures with disorder and next-nearest-neighbor coupling

We theoretically investigate the quantum correlations of nonclassical states in disordered optical waveguides with next-nearest-neighbor (second-order) coupling. We find that single-particle states from different initial positions exhibit similar behavior at specific second-order coupling strengths. At the same time, entangled bosons display correlations that are either analogous to or mirror-symmetric to those of bosons and fermions. We numerically calculate the interparticle distance probabilities of both planar and circular structures and show that their distinct boundary conditions produce unique correlation patterns. In certain cases, bosons are less likely to occupy the same site and single-particle states show asymmetric probability distributions. The effects of second-order coupling and disorder act to cancel out these nontrivial features. Nonclassical states have found numerous applications in integrated quantum photonics. Furthermore, in practical scenarios, disorder is unavoidable, and second-order coupling becomes crucial for light-matter interactions, polymer chains, magnetic materials, non-Hermitian Hamiltonians, topologically nontrivial systems, spin chains, and so on. Their combined effects across diverse physical systems and experimental platforms signify the broader importance of our work.