Realisation of Protected Cat Qutrit via Engineered Quantum Tunnelling

Engineering quantum tunnelling in phase space has emerged as a viable method for creating a protected qubit with biased-noise properties. A promising approach is to combine a Kerr nonlinearity with multi-photon transitions, resulting in a system known as a Kerr parametric oscillator (KPO). In this work, we implement a three-photon KPO and explore its potential as a protected qutrit. We confirm quantum coherence by demonstrating three-photon Rabi oscillations and performing direct Wigner function measurements that reveal three-component cat-like states. We observe breathing-like dynamics in phase space, arising from exotic temporal interference between the qutrit and excited states. The frequency of this interference corresponds to the energy gap between the qutrit and excited manifolds, thereby providing an experimental hallmark of qutrit space protection. We also identify a higher-order pump term as the main mechanism suppressing photon occupation; mitigating this term is necessary to maximize protection. Our findings elucidate the basic quantum properties of the three-photon KPO and establish the first step toward its use as an alternative qutrit platform.