Quantum theory of topological phase transitions for cavity polaritons in optical metasurfaces

Topological states of matter exhibit fundamental properties that are protected by their symmetries and cannot be easily altered by small perturbations. This feature makes them the ideal candidates for hosting excitations able to carry information in a topologically protected way. While this seems ideal in view of potential applications in information technology, it can also represent a drawback as the topological phases, once imprinted in the design of a system by breaking specific symmetries, lack the tunability expected from conventional computing and IT devices. In this project we will explore topological phases of matter in optical metasurfaces - artificial two-dimensional materials realised by designing specific symmetries in arrays of sub-wavelength optical resonators (e.g. a planar assembly of interacting nano-scale antennas). By means of the quantum formalism developed by Hopfield, we will study the bandstructure and fundamental topological properties of the hybrid light-matter excitations of the system (polaritons). Due to the hybrid nature of polaritons as half-light half-matter quasiparticles, we will aim to tune their bandstructure and topological properties by modifying the photonic environment alone via an enclosing planar optical cavity. This will allow us to realise topological phase transitions while preserving the lattice symmetries fixed by design at the fabrication stage of the metasurface. We will explore the physical properties of the interfaces between inequivalent topological phases of polaritons in the metasurface, as well as the effect of disorder and lattice distortions on the polaritonic topological phases. In this context we will analyse the role of metallic gates as a tool to tune the bandstructure of polaritons, launch them, guide their propagation and amplify them via selective parametric resonances.