Building quantum dots and Laughlin puddles from optical photons

Building a synthetic material out of light requires control of three basic ingredients: photon dispersion, interactions, and the population within the (many-)photon state space. Confining optical photons in an optical cavity allows tailoring the single particle Hamiltonian. A single mode cavity provides a zero-dimensional quantum dot, while degenerate multimode cavities give rise to one- or two-dimensional harmonic confinement and even an effective magnetic field. Hybridizing cavity photons with Rydberg excitations of a cold atomic gas turns non-interacting photons into strongly-interacting cavity Rydberg polaritons, quasiparticles which inherit their motional dynamics from their photonic component and gain strong interactions from their Rydberg component. In a quantum dot we observe these interactions giving rise to strong anti-bunching of photons travelling through the system. When we grant polaritons access to a degenerate Landau level of cavity states, they collide and reorder into topologically nontrivial material states. Ongoing work to engineer dissipation in this system to autonomously cool into a topologically ordered ground state will permit the preparation of large topological materials and the direct manipulation of anyonic excitations.