Measurement of the Crossover from Photon Ordering to Delocalization in a Driven-Dissipative Superconducting Resonator System

Sizeable photon-photon interactions in networks of nonlinear oscillators enable the study of strongly correlated photons in non-equilibrium quantum many-body systems. We present a system composed of two superconducting resonators, coupled nonlinearly by a superconducting quantum interference device (SQUID). By applying a parametrically modulated magnetic flux we control the linear photon hopping rate between the two resonators and its ratio with the cross-Kerr rate. When increasing the hopping rate we observe a fully controllable crossover in the spatial correlations of the photonic fields of the two resonators, from photon self-ordering to delocalization of photons. The presented parametric coupling scheme is intrinsically robust to frequency disorder and may therefore prove useful for realizing larger-scale resonator arrays, and in turn facilitate active control of extended correlated quantum gases for the purpose of emulating other less accessible quantum systems.