New Approaches for Quantum Many-Body Physics with Ultracold Atomic Systems

In the emerging field of quantum simulation, where well-controlled quantum systems are used to experimentally investigate interesting many-body phenomena, ultracold atoms and ions are proving to be an excellent physical platform. I describe directions for developing experiments that could further increase the complexity of many-body physics accessible in atomic systems. The bulk of the talk focuses on my preliminary demonstrations of integer-spin chains in ion traps, along with a discussion of the limitations of the initial experiments and the apparatus I plan to build for implementing interactions among particles of spin>1/2 and reading out the spin projection of each ion in a single shot. I then discuss another system which holds potential for creating many-body systems coupling atomic spin and motion to photonic modes, constituting a more complicated Hilbert space than is accessible with trapped ions. This hybrid quantum system consists of neutral atoms individually trapped in optical tweezers, then coupled to nanofabricated optical resonators. I describe my current efforts to demonstrate heralded two-atom interactions with this platform, along with an outlook on new strategies it enables for studying long-range interacting quantum systems.