Exploring Landau Levels in Curved Space

I will present recent work realizing topological phases of photons, both in curved space, and in lattices. The talk will focus on our recent exploration of Landau levels on a conical surface, generated using a non-planar (twisted) optical resonator to induce a synthetic magnetic field for optical photons, and employed to validate the famous Wen-Zee action. I will then discuss recent results demonstrating strong photon-photon interactions mediated by resonator Rydberg-electromagnetically induced transparency (EIT), and techniques we are developing to assemble topological few-body states both photon-by-photon, and through microscopic devices engineered for photon thermalization. I will conclude with our recent observation of time-resolved helical edge dynamics in Z_2 topological circuit lattices, and a T-broken extension in the microwave domain using arrays of 3D cavities and circuit quantum electrodynamics techniques. This work showcases the unique possibilities for Hamiltonian engineering and control in the photonic sector, a provides a taste of upcoming breakthroughs in engineering quantum materials from photons.