Abstract
Synchronization occurs ubiquitously in nature. The van der Pol oscillator has been a favorite model to investigate synchronization. Here we study the oscillator in the deep quantum regime, where nonclassical effects dominate the dynamics. Our results show: (i) squeezed driving loses its effect, (ii) noise boosts synchronization, (iii) synchronization is bounded, and (iv) the limit-cycle is insensitive to strong driving. We propose a synchronization measure and analytically calculate it. These results reflect intrinsic differences between synchronization in the quantum and deep quantum regimes.
Highlights
From coupled metronomes [1,2,3] to brain activity [4] and jet-lag [5], synchronization is used to explain countless phenomena in nature
In this paper we have investigated the quantum van der Pol oscillator in the deep quantum regime
The regime was identified as γ2/γ1 10 motivated by physical phenomena: We found that squeezing provides a synchronization boost in the quantum regime, but in the deep quantum regime the effect is strongly suppressed compared to the robust synchronization from harmonic driving
Summary
From coupled metronomes [1,2,3] to brain activity [4] and jet-lag [5], synchronization is used to explain countless phenomena in nature. Synchronous behavior of a quantum system without a limit cycle does not necessarily count as a quantum analog of the well-known classical synchronization, since the phase of the system is not free [3] To this end, the most commonly studied model is the quantum van der Pol oscillator in the weakly nonlinear regime [9,10], known as the quantum Stuart-Landau oscillator [41]. With pure harmonic driving of the qvdP (η = 0), we can obtain an analytical approximation for the master equation in the deep quantum regime. To this end, we make the following ansatz for the density matrix in the Fock basis:.
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