Synchronizing microwave cQED limit-cycle oscillators

TL;DR

This paper investigates synchronization phenomena in microwave cQED limit-cycle oscillators driven by a hybrid electron-photon system, revealing bifurcations, limit-cycle behavior, and synchronization conditions through theoretical modeling.

Contribution

It introduces a novel analysis of quantum limit-cycle oscillators in microwave cQED systems, including bifurcation, synchronization, and a derived nonlinear photon Keldysh action.

Findings

Hopf bifurcation at critical electron-photon coupling

Synchronization of two limit-cycle resonators via a DQD

Agreement between Keldysh and Lindblad approaches in the Markovian limit

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.