Strongly interacting fluids in a Bose-Hubbard circuit: Observables

In recent years, circuit QED has proven to be a rich testbed for studying many-body phenomena in synthetic photonic materials. We assemble a 1D Bose Hubbard lattice for microwave photons using a chain of capacitively coupled transmon qubits, with strong photon interactions mediated by the transmon anharmonicity. In this second part of the talk, we discuss our results in probing the static and dynamical properties of the adiabatically prepared fluid. We characterize the long-range order in the lattice by measuring two-body density correlations, highlighting the statistics for the separation between two photons. Going beyond nonlocal correlations, we probe the global entanglement from single-site tomography and average the purity over the whole lattice. Finally, we access out-of-equilibrium transport properties by locally modulating the lattice potential and measuring the spectral response in terms of heat absorption and AC susceptibility, offering a direct probe of the low lying density of states of the strongly interacting fluid.