Synchronizing microwave cQED limit-cycle oscillators

• URL: http://arxiv.org/abs/2511.07140v2
• Date: Tue, 18 Nov 2025 17:38:12 GMT
• Title: Synchronizing microwave cQED limit-cycle oscillators
• Authors: Cecilie Hermansen, Jens Paaske,
• Abstract summary: We explore the properties of a driven dissipative electron-photon hybrid system based on superconducting microwave resonators coupled resonantly to a voltage-biased double quantum dot (DQD)<n>We show that two such limit-cycle resonators coupled via the same voltage-biased DQD synchronize for small enough frequency detuning.<n>A nonlinear photon Keldysh action is derived by perturbation theory in the effective circuit fine-structure constant, and the limit-cycle dynamics is analyzed in terms of resulting saddle-point, and Fokker-Planck equations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Self-sustained oscillators play a central role in the stabilization and synchronization of complex dynamical systems. A number of different physical systems are currently being investigated to clarify the importance of such active components in the quantum realm. Here we explore the properties of a driven dissipative electron-photon hybrid system based on superconducting microwave resonators coupled resonantly to a voltage-biased double quantum dot (DQD). First, we establish a Hopf bifurcation at a critical value of the electron-photon coupling, beyond which an effective negative friction sustains steady limit-cycle oscillations of individual resonators. Second, we show that two such limit-cycle resonators coupled via the same voltage-biased DQD synchronize for small enough frequency detuning. A nonlinear photon Keldysh action is derived by perturbation theory in the effective circuit fine-structure constant, and the limit-cycle dynamics is analyzed in terms of resulting saddle-point, and Fokker-Planck equations. In the Markovian limit of infinite bias voltage, these results are shown to agree well with the solution of a corresponding Lindblad master equation for the DQD resonator system.

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