Topological physics exploits concepts from geometry and topology to implement systems capable of guiding waves in an unprecedented fashion. These ideas have led to the development of photonic topological insulators, which are optical systems whose eigenspectral topology allows the creation of light states that propagate along the edge of the system without any coupling into the bulk or backscattering even in the presence of disorder. Indeed, topological protection is a fully coherent effect, and it is not clear to what extent topological effects endure when the wavefronts become partially coherent. Here, we study the interplay of topological protection and the degree of spatial coherence of classical light propagating in disordered photonic topological insulators. Our results reveal the existence of a well-defined spectral window in which partially coherent light is topologically protected. This opens up the design space to a wider selection of light sources, possibly yielding smaller, cheaper, and more robust devices based on the topological transport of light.

Activating transitions between internal states of physical systems has emerged as an appealing approach to create lattices and complex networks. In such a scheme, the internal states or modes of a physical system are regarded as lattice sites or network nodes in an abstract space whose dimensionality may exceed the systems’ apparent (geometric) dimensionality. This introduces the notion of synthetic dimensions, thus providing entirely novel pathways for fundamental research and applications. Here, we analytically show that the propagation of multiphoton states through multiport waveguide arrays gives rise to synthetic dimensions where a single waveguide system generates a multitude of synthetic lattices. Since these synthetic lattices exist in photon-number space, we introduce the concept of pseudo-energy and demonstrate its utility for studying multiphoton interference processes. Specifically, the spectrum of the associated pseudo-energy operator generates a unique ordering of the relevant states. Together with generalized pseudo-energy ladder operators, this allows for representing the dynamics of multiphoton states by way of pseudo-energy term diagrams that are associated with a synthetic atom. As a result, the pseudo-energy representation leads to concise analytical expressions for the eigensystem of N photons propagating through M nearest-neighbor coupled waveguides. In the regime where N≥2 and M≥3, nonlocal coupling in Fock space gives rise to hitherto unknown all-optical dark states that display intriguing nontrivial dynamics.

Exceptional points (EPs) are degeneracies of non-Hermitian operators where, in addition to the eigenvalues, the corresponding eigenmodes become degenerate. Classical and quantum photonic systems with EPs have attracted tremendous attention due to their unusual properties, topological features, and an enhanced sensitivity that depends on the order of the EP, i.e., the number of degenerate eigenmodes. Yet, experimentally engineering higher-order EPs in classical or quantum domains remain an open challenge due to the stringent symmetry constraints that are required for the coalescence of multiple eigenmodes. Here, we analytically show that the number-resolved dynamics of a single, lossy waveguide beam splitter, excited by N indistinguishable photons and post-selected to the N-photon subspace, will exhibit an EP of order N+1. By using the well-established mapping between a beam splitter Hamiltonian and the perfect state transfer model in the photon-number space, we analytically obtain the time evolution of a general N-photon state and numerically simulate the system’s evolution in the post-selected manifold. Our results pave the way toward realizing robust, arbitrary-order EPs on demand in a single device.