The driven Kerr parametric oscillator, of interest to fundamental physics and quantum technologies, exhibits an excited state quantum phase transition (ESQPT) originating in an unstable classical periodic orbit. The main signature of this type of ESQPT is a singularity in the level density in the vicinity of the energy of the classical separatrix that divides the phase space into two distinct regions. The quantum states with energies below the separatrix are useful for quantum technologies, because they show a catlike structure that protects them against local decoherence processes. In this work, we show how chaos arising from the interplay between the external drive and the nonlinearities of the system destroys the ESQPT and eventually eliminates the cat states. Our results demonstrate the importance of the analysis of theoretical models for the design of new parametric oscillators with ever larger nonlinearities.

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• Circuit quantum electrodynamics
• Nonlinear optics
• Open quantum systems & decoherence
• Optical chaos
• Optical parametric oscillators & amplifiers
• Quantum information architectures & platforms
• Quantum memories
• Quantum phase transitions