Can a material be made of light? To answer this, we first ask what is necessary for a material to form, and then how to go about engineering each of these properties for photons. We trap photons inside of a curved-mirror optical resonator, which harmonically traps the transverse motion of photons and imbues them with an effective mass. By making the resonator nonplanar, we introduce an effective magnetic field for (charge neutral) photons, and explore the structure of the resulting Landau levels. At this point we have made our first material system, an integer quantum Hall material, and we introduce some of its interesting topological properties.
Adding repulsive interactions—so that photons collide with each other rather than passing right through each other—opens up a zoo of interesting material systems. I will briefly present how we engineer such collisions by hybridizing resonator photons with Rydberg excitations of a cold Rubidium gas. We observe the effect of these collisions through correlations in the transmission of photons through the resonator. Finally, we will conclude with our current progress towards combining all these ingredients to explore the physics of a fractional quantum Hall material using light.