Parametrically driven oscillators can emerge as a basis for the next generation of qubits. Classically, these systems exhibit two stable oscillatory states with opposite phases. Upon quantization, these states turn into a pair of closely spaced Floquet states, which can serve as the logical basis for a qubit. However, interaction with the environment induces phase-slip events which set a limit on qubit coherence. Such phase slips persist even at zero temperature due to a mechanism known as quantum activation. In contrast to conventional tunneling, the quantum activation is described by a real-time instanton trajectory in the complexified phase space of the system. In this work, we show that the phase-slip rate is exponentially sensitive to weak ac perturbations. The spectrum of the system's response—captured by the so-called logarithmic susceptibility—enables a direct observation of characteristic features of real-time instantons. Studying this spectrum suggests new means of efficient qubit control.

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• Instantons
• Mesoscopics
• Open quantum systems & decoherence
• Parametric resonance
• Quantum control
• Floquet systems
• Nanomechanical devices
• Superconducting qubits
• First passage problems
• Lindblad equation
• Semiclassical methods