Light propagating in linear and nonlinear waveguide lattices exhibits behaviour characteristic of that encountered in discrete systems. The diffraction properties of these systems can be engineered, which opens up new possibilities for controlling the flow of light that would have been otherwise impossible in the bulk: these effects can be exploited to achieve diffraction-free propagation and minimize the power requirements for nonlinear processes. In two-dimensional networks of waveguides, self-localized states--or discrete solitons--can travel along 'wire-like' paths and can be routed to any destination port. Such possibilities may be useful for photonic switching architectures.

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Quantum walks of correlated particles offer the possibility to study large-scale quantum interference, simulate biological, chemical and physical systems, and a route to universal quantum computation. Here we demonstrate quantum walks of two identical photons in an array of 21 continuously evanescently-coupled waveguides in a SiOxNy chip. We observe quantum correlations, violating a classical limit by 76 standard deviations, and find that they depend critically on the input state of the quantum walk. These results open the way to a powerful approach to quantum walks using correlated particles to encode information in an exponentially larger state space.With origins dating back to observations by Lucretius in 60BC and Brown in the 1800's, random walks are a powerful tool used in a broad range of fields from genetics to economics [1]. The quantum mechanical analoguequantum walks [2, 3]-corresponds to the tunnelling of quantum particles into several possible sites, generating large coherent superposition states and allowing massive parallelism in exploring multiple trajectories through a given connected graph (eg. Fig. 1). This quantum state evolution is a reversible (unitary) process and so requires low noise (decoherence) systems for observation. In contrast to the diffusive behaviour of (classical) random walks, which tend towards a steady state, the wave function in a quantum walk propagates ballistically (Fig. 2(c)). These features are at the heart of new algorithms for database-search [4], random graph navigation, models for quantum communication using spin chains [5], universal quantum computation [6] and quantum simulation [7].Quantum walks have been demonstrated using nuclear magnetic resonance [8,9], phase [10,11] and position [12] space of trapped ions, the frequency space of an optical resonator [13], single photons in bulk [14] and fibre [15] optics and the scattering of light in coupled waveguide arrays [16]. However, to date, all realisations have been limited to single particle quantum walks, which have an exact mapping to classical wave phenomena [17], and therefore cannot provide any advantage from quantum effects (note that the quantum walk with two trapped ions [11] encodes in the centre of mass mode and is therefore effectively a single particle quantum walk on a line). Indeed single particle quantum walks have been observed using classical light [16,18]. In contrast, for quantum walks of more than one indistinguishable particle, classical theory no longer provides a sufficient description-quantum theory predicts that probability amplitudes interfere leading to distinctly non-classical correlations [19,20]. This quantum behaviour gives rise to a computational advantage in quantum walks of two identical particles, which can be used to solve the graph isomorphism problem for example [21]. The major challenge associated with realising quantum walks of correlated particles is the need for a low decoherence system that preserves their non-classical features.The intrinsically low decoherence properti...

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We experimentally investigate the evolution of linear and nonlinear waves in a realization of the Anderson model using disordered one-dimensional waveguide lattices. Two types of localized eigenmodes, flat-phased and staggered, are directly measured. Nonlinear perturbations enhance localization in one type and induce delocalization in the other. In a complementary approach, we study the evolution on short time scales of delta-like wave packets in the presence of disorder. A transition from ballistic wave packet expansion to exponential (Anderson) localization is observed. We also find an intermediate regime in which the ballistic and localized components coexist while diffusive dynamics is absent. Evidence is found for a faster transition into localization under nonlinear conditions.