Cavity QED and quantum spin liquids

A prescient vision that motivated the last years of Jeff Kimble's research was that quantum optics and many-body physics would interface together to create an exciting new research frontier. Here, I discuss early collaborative work with Kimble that inspired me to dive into the field of many-body quantum optics, where we studied precisely positioned atoms coupled to photonic devices. Such systems naturally lead to quantum spin models featuring long-range coherent interactions and collective dissipation. However, an open question that largely persists even today is how such unique ingredients might actually induce strongly correlated physics, especially given that long-range coherent and dissipative interactions tend to favor collective spin or mean-field behavior. I discuss our recent work that attempts to find paradigms that evade mean-field physics. In particular, I show how long-range interactions can be used to project systems into S=0 total angular momentum subspaces. This subspace is highly degenerate, but contains interesting spin states such as resonating valence bond (RVB) spin liquids. I then show how additional short-range interactions, for example due to atomic Rydberg interactions, can be used to pull out an RVB spin liquid as the unique ground state.