Period-tripling subharmonic oscillations in a driven superconducting resonator

Abstract

We have observed period-tripling subharmonic oscillations in a driven superconducting coplanar waveguide resonator operated in the quantum regime, ${k}_{B}T\ensuremath{\ll}\ensuremath{\hbar}\ensuremath{\omega}$. The resonator is terminated by a tunable inductance that provides a Kerr-type nonlinearity. We detected the output field quadratures at frequencies near the fundamental mode, $\ensuremath{\omega}/2\ensuremath{\pi}\ensuremath{\sim}5\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}$, when driving the resonator with a current at $3\ensuremath{\omega}$, with amplitude exceeding an instability threshold. We observed three stable radiative states with equal amplitudes, phase shifted by $2\ensuremath{\pi}/3$ rad, red detuned from the fundamental mode. The down-conversion from $3\ensuremath{\omega}$ to $\ensuremath{\omega}$ is strongly enhanced by near-resonant excitation of the second mode of the resonator and the cross-Kerr effect. Our experimental results are in quantitative agreement with a model for the driven dynamics of two coupled modes.