In this talk I will discuss recent results from a collaboration between the Simon & Schuster labs, where we have developed techniques for assembling quantum matter from strongly interacting microwave photons. Beginning with a description of the platform - an array of capacitively coupled transmon qubits acting as a Hubbard-regime lattice for photons — I will motivate the challenges associated with teaching photons to order into materials. From here, I will describe two experiments: (1) assembly of mott insulators by coupling to an non-markovian reservoir capable of cooling the system whilst simultaneously injecting photons; and (2) assembly of photon fluids by controlled introduction and removal of disorder + the ability to extend this technique to assembly of superpositions of superfluids — photonic cat states. I will conclude with prospects for assembly of topologically ordered matter, and a brief overview of our other collaborative efforts.
