Effects of nonlinearity in the emission spectrum of the driven nonlinear oscillator

Motivated by many experiments on nonlinear driven systems realized using superconducting circuits we investigate the properties of a coherently driven nonlinear resonator. By using Josephson junctions in superconducting circuits, strong nonlinearities can be engineered, which lead to a relatively low number of photons in the resonator and the appearance of pronounced nonlinear effects. Based on a master equation approach, which takes into account the quantum nature of noise, we determine the emission spectrum and observe for typical circuit QED parameters, in addition to the primary side-peaks, second-order peaks not predicted by a linearized theory.