Driven quantum nonlinear resonators: new exact solution techniques and generalized photon blockade

Interacting driven-dissipative quantum resonators are at the forefront of research in quantum optics and quantum computing with superconducting circuits. We develop a new theoretical approach that allows one to non-perturbatively find the steady states of such systems. Our approach uncovers surprising phenomena in systems with an unusual three-photon coherent drive. This includes a new kind of generalized photon blockade effect, where interference causes a sharp cut-off in the system’s photon-number distribution despite without requiring extremely strong nonlinearity. This is distinct from standard photon blockade (which requires a strong nonlinearity), or the so-called “unconventional photon blockade” (which does not completely suppress high photon number states). We also describe a new kind of quantum bistability in these systems, which we can understand as a kind of interference between pairs of holomorphic functions in phase space. The effects we describe are well within the reach of current experiments in circuit QED, and could be harnessed for a variety of applications in quantum information processing.