S, P, D… BEC…  Easy as I, II, III: Pairing Games in a Cavity

Many quantum materials display striking behavior because different types of order compete with one another. This competition is especially important in unconventional and topological superconductors, where the symmetry of electron pairing can produce robust edge currents and other exotic effects—yet it remains difficult to observe and control directly.

In this talk, I will introduce a quantum simulation platform based on atoms trapped in a two-dimensional optical lattice inside an optical cavity, where light-mediated interactions can be precisely engineered and continuously monitored. By tailoring cavity-induced couplings between atomic pseudospins, the simulator emulates momentum-dependent pairing channels and realizes pairing ranging from conventional s-wave to competing chiral p+ip and d+id orders. I will then show how this minimal and fully tunable platform enables controlled state preparation and direct measurement of superconducting order parameters, revealing phases both in and out of equilibrium, with either a single dominant pairing channel or competing channels. This approach opens new opportunities to explore nonequilibrium topological superconductivity in a clean, controllable setting beyond what is readily accessible in real materials and in ultracold gases with purely contact interactions.