# Quantum Walks in Photonic Lattices

Random quantum walk is the process describing the motion of a quantum particle that hops randomly, yet coherently, from site to site on a lattice. The coherent motion induces a big difference between quantum walks, for example the motion of an electron in a lattices, and classical random walks, that are responsible for processes such as molecular diffusion. We study quantum walks of photons in 'photonic lattices' that are made of arrays of optical waveguides that are close enough to allow photons to hop between them. Such lattices have been used for more than a decade to study some of the most basic phenomena of wave propagation in periodic and quasi-periodic structures, from Bloch Oscillations to Anderson Localization. While most work with photonic lattices have studied wave propagation using coherent laser light, we have shown that they could also serve as an excellent platform for the study of quantum dynamics, and in particular of quantum walks. We have extended this concept to more complex random walks of several particles, and have shown that such walks by indistinguishable particles lead to new and surprising effects on the quantum correlations of the co-propagating walkers in periodic lattices. Even more surprises are found when the quantum walkers move in a disordered lattice where the particles are also constrained via Anderson localization, and I will present recent experiments on such systems.