We study microwave response of a Josephson parametric oscillator consisting of a superconducting transmission-line resonator with an embedded dc-SQUID. The dc-SQUID allows to control the magnitude of a Kerr nonlinearity over the ranges where it is smaller or larger than the photon loss rate. Spectroscopy measurements reveal the change of the microwave response from a classical Duffing oscillator to a Kerr parametric oscillator in a single device. In the single-photon Kerr regime, we observe parametric oscillations with a well-defined phase of either 0 or π, whose probability can be controlled by an externally injected signal.
@article{arxiv.2010.02621,
title = {Spectroscopic observation of the crossover from a classical Duffing oscillator to a Kerr parametric oscillator},
author = {T. Yamaji and S. Kagami and A. Yamaguchi and T. Satoh and K. Koshino and H. Goto and Z. R. Lin and Y. Nakamura and T. Yamamoto},
journal= {arXiv preprint arXiv:2010.02621},
year = {2022}
}