Three-photon Kerr Parametric Resonator Dynamics in the Quantum Regime

Driven-dissipative Kerr resonators exhibit intriguing classical and quantum dynamics. In this work, we explore the three-photon Kerr parametric resonator (3KPR), where a Kerr-nonlinear resonator is driven by a parametric three-photon pump. As the pump strength increases, the system’s eigenstates become degenerate in triplets. At the mean field level, this manifests as a spontaneous Z₃-symmetry breaking. Furthermore, for specific pump-resonator detuning values, the 3KPR Hamiltonian admits exact analytical eigenstate solutions, which can be approximated by superpositions of displaced squeezed number states at large pump amplitudes. In this talk, I will introduce this system and discuss its potential applications as a robust qutrit memory as well as a possible circuit QED realization.