Spectroscopic Observation of Crossover from Classical Duffing Oscillator to Kerr Parametric Oscillator*

A Kerr parametric oscillators (KPO) is a parametric oscillator in the single-photon Kerr regime, where the Kerr nonlinearity is larger than the photon loss rate (but not as large as transmon qubits). This regime is relatively unexplored, and the KPOs have a wide range of potential applications such as deterministic generation of Schrödinger cat state [1] and quantum computation [2]. 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.

[1] H. Goto, et al., Phys. Rev. A 99, 023838 (2019).
[2] H. Goto, Sci. Rep. 6, 21686 (2016).