Synchronization phenomena occur throughout nature. The van der Pol oscillator has been a paradigmatic model to investigate synchronization. Here we study the oscillator with additional single-photon dissipation in the deep quantum regime (defined to be ${\gamma }_2/{\gamma }_1\gtrsim 10$), and we contrast it with the quantum regime at ${\gamma }_2/{\gamma }_1\approx 1$. Our results show that in this regime: (i) the effect of squeezed driving effect on frequency entrainment is strongly suppressed, (ii) single-photon dissipation boosts synchronization, (iii) synchronization is bounded, and (iv) the limit-cycle is robust and insensitive to strong driving. We use these physical properties to define the crossover to the deep quantum regime. We also propose a synchronization measure based on directional statistics which is analytically calculated. These results reflect the intrinsic physical differences between synchronization in the quantum and deep quantum regimes.

• Received 20 February 2020
• Accepted 21 August 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033422

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society