Demonstration of programmable quantum simulations of lattice models using a superconducting parametric cavity

There has been a growing interest in realizing quantum simulators for important physical systems where perturbative methods are ineffective. The scalability and flexibility of circuit quantum electrodynamics (cQED) make it a promising platform for implementing various types of simulators, including lattice models of strongly-coupled field theories. With this in mind, we use a multimode superconducting parametric cavity to create programmable lattices of bosonic modes by parametrically pumping at mode-difference frequencies. The choice of pump frequencies allows changing the graph of the lattice in situ. Further, the resulting hopping terms induced between the modes can be made complex by controlling the relative phases of the parametric drives. This enables us to study a wide variety of interesting lattice models. For instance, controlling the total loop phase in closed plaquettes allows us to simulate the motion of particles in a static gauge field, including producing nonreciprocal transport. The system can also realize models with topological features such as the bosonic Creutz ladder. In this talk, we present experimental results on a variety of different small lattice models.