| Summary: | The propagation of light waves across a periodic array of evanescently coupled optical waveguides can be described by a Schr¨odinger-like equation for a particle in a periodic potential. This mapping allows us to investigate the dynamics of electrons in a crystalline solid using an artificial crystal of optical waveguides, known as a photonic lattice. The unique capabilities of ultrafast laser inscription enable us to design, fabricate and precisely control various properties of a photonic lattice. Here, we focus on the experimental construction of the Hamiltonians associated with various complex quantum systems using engineered photonic lattices, and then measure the time evolution of a given input state. In this photonic platform, we experimentally observe various single particle effects known from solid-state physics, such as the localised states associated with flat-band lattice geometries, localised Wannier-Stark states, photon-assisted tunnelling and the anomalous topological edge modes in slowly-driven lattices. Specific phenomena associated with particle interactions, such as the dynamics of two interacting particles in a one-dimensional lattice with static and sinusoidally driven Hubbard Hamiltonian, is also investigated. The experimental results presented here will be of interest to a large community, including physicists working on photonics, quantum optics, cold atomic gases, and condensed-matter physics.
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