Period-tripling subharmonic oscillations in a driven superconducting resonator

We have observed period-tripling subharmonic oscillations, in a superconducting coplanar waveguide resonator operated in the quantum regime, $k_{B}T\ll \mathrm{\hslash }\omega$. 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, $\omega/2\pi \sim 5,$GHz,whentheresonatorwasdrivenbyacurrentat$3\omega$ with an amplitude exceeding an instability threshold. The output radiation was red-detuned from the fundamental mode. We observed three stable radiative states with equal amplitudes and phase-shifted by ${120}^{\circ }$. The downconversion from $3\omega$ to $\omega$ is strongly enhanced by 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.