Geometrical dimensionality is known to have a great impact on the fundamental characteristics of physical systems, from the stability of planetary orbits to the occurrence of Anderson localisation. Importantly, accessing higher dimensions is central to the fundamental enhancement of performance in many applications, such as deep neural network and scalable quantum computation. While technological advances enable the realisation of integrated photonic structures interacting with light analogous to electronic lattices, the direct use of such usually planar structures restricts behaviours of photonic states to be within low-dimensional effects. Recently, synthetic lattices appear as an emerging and rapidly growing topic in photonics, where artificial engineering of discrete potentials is employed to lift up limitations imposed by the geometry. Yet it remains unknown in many aspects how such synthetic lattices can be utilized to facilitate multidimensional photonics.

In this seminar, I will summarise the theoretical and experimental study of multidimensional photonics that uses synthetic lattices for the manipulation and measurement of both classical and quantum photonic states. More specifically, our synthetic lattices are characterised by judiciously tailored transformations and mappings. First, I will introduce a controllable and all-optical platform that can synthesise dimensions by mapping discrete frequency components with long-range interactions to higher dimensional space. Then, I will discuss a new paradigm to access higher dimensions using a tailored iso-spectral mapping that enables certain excitation dynamics in arbitrary-dimensional networks to be exactly reproduced in practical one-dimensional lattices. Then, I will outline a new concept of using advanced imaging to map out entangled quantum states based on special transformations designed on nanostructured metasurfaces. Finally, such transformations are brought to integrated photonic circuits for the inline detection and measurement of multiphoton quantum states, making it possible to pinpoint issues of large quantum networks in real-time.