Displacement oscillator: High order photon-photon interactions in a superconducting circuit (Part 1)

A quantum harmonic oscillator perturbed by a Josephson junction nonlinearity has become ubiquitous in quantum science and engineering. In the usual regime, the fluctuations of the superconducting phase across the junction are small and the Josephson nonlinearity reduces to the Kerr effect, thereby enabling amplification of microwave signals and encoding of quantum information. In this experiment, we explore the new regime of large phase fluctuations, where the Josephson cosine potential is dominated by mixing terms even higher than fourth order. We expect peculiar effects in this extreme limit, such as the alternation of the sign of the oscillator frequency shift for each added photon, and even nonlocal quantum dynamics. In this two-part talk, we present the theoretical model of the system as well as experimental progress.