Spectroscopic observation of the crossover from a classical Duffing oscillator to a Kerr parametric oscillator

TL;DR

This paper investigates the transition of a superconducting microwave resonator from classical Duffing oscillator behavior to quantum Kerr parametric oscillations, demonstrating control over nonlinearities and phase states.

Contribution

It experimentally demonstrates the crossover from classical to quantum nonlinear regimes in a Josephson parametric oscillator with tunable Kerr nonlinearity.

Findings

Spectroscopy shows the transition from Duffing to Kerr oscillator behavior.

Observation of phase-controlled parametric oscillations in the quantum regime.

Tunable Kerr nonlinearity relative to photon loss rate.

Abstract

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 $\pi$, whose probability can be controlled by an externally injected signal.