We analyze the dynamics of the Rabi model describing interactions of a qubit with a single soft-mode oscillator. We show that the model with a slightly violated parity generates symmetric Schrödinger cat states of the oscillator, which suddenly perish in a spontaneous unitary process similar to the measurement-induced wave-function collapse. The effect is sufficiently robust to be tested experimentally, e.g., with trapped ions, macroscopic mechanical oscillators, or superconducting circuits.

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• Quantum harmonic oscillator
• Quantum measurements
• Quantum superposition
• Semiclassical physics
• Rabi model