Topological and fracton order in Rydberg atom arrays

Theoretical studies over the past decades have unearthed a rich picture of strongly-interacting quantum states of matter with exotic order. These highly-entangled states are interesting, both at a conceptual level, as well as a tool for quantum metrology or quantum computation purposes. However, their experimental realization and detection has proven to be challenging. In this talk, I will review some of our proposals for realizing these states in Rydberg atom tweezer arrays. The ability to control individual atoms---strongly-interacting over a wide distance---make these arrays an ideal platform for realizing exotic many-body quantum states, whose nonlocal order parameters can be probed by imaging the whole array. We will explore the whole spectrum of short- and long-range entanglement: from symmetry-protected topological phases, over cat states, to intrinsic topological order and even 3D fracton states.