Synchronization boost with single-photon dissipation in the deep quantum regime

Abstract

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 γ_{2}/γ_{1}≳10), and we contrast it with the quantum regime at γ_{2}/γ_{1}≈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.