It is shown, both theoretically and experimentally, that one-dimensional quasicrystals are assigned two-dimensional Chern numbers and, respectively, exhibit topologically protected boundary states equivalent to the edge states of a two- dimensional quantum Hall system.Expand

An intermediate regime is found in which the ballistic and localized components coexist while diffusive dynamics is absent and evidence is found for a faster transition into localization under nonlinear conditions.Expand

The output pattern resulting from the injection of two correlated photons possess quantum features, indicating that the photons retain their correlations as they walk randomly through the waveguide array, allowing scale-up and parallel searches over many possible paths.Expand

Environmental noise and disorder play critical roles in quantum particle and wave transport in complex media, including solid-state and biological systems. While separately both effects are known to… Expand

Using interacting bosonic atoms in an optical lattice, this work directly observed fundamental effects such as the emergence of correlations in two-particle quantum walks, as well as strongly correlated Bloch oscillations in tilted optical lattices.Expand

The results demonstrate that waveguide lattices can be used as a robust and highly controllable tool for manipulating quantum states, and offer new ways of studying the quantum properties of light.Expand

It is shown that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially an implementation of quantum walks.Expand

The observation of the signature of a localization phase transition for light in one-dimensional quasiperiodic photonic lattices is reported by directly measuring wave transport inside the lattice, and the effect of focusing nonlinear interaction on the propagation increases the width of the localized wave packets.Expand

The predicted quantum correlations between noninteracting particles evolving simultaneously in a disordered medium show oscillatory correlations within the localization length and can be observed in Anderson localization of nonclassical light and ultracold atoms.Expand

We study the effect of interactions on the propagation of quantum correlations in the bosonic two-body quantum walk. The combined effect of interactions and Hanbury Brown\char21{}Twiss interference… Expand