Quantum Synchronization of Quantum van der Pol Oscillators with Trapped Ions

Abstract

The van der Pol oscillator is the prototypical self-sustained oscillator and has been used to model nonlinear behavior in biological and other classical processes. We investigate how quantum fluctuations affect phase locking of one or many van der Pol oscillators. We find that phase locking is much more robust in the quantum model than in the equivalent classical model. Trapped-ion experiments are ideally suited to simulate van der Pol oscillators in the quantum regime via sideband heating and cooling of motional modes. We provide realistic experimental parameters for 171Yb+ achievable with current technology.

Synchronization of micromasers

“…Indeed, comparisons of numerical calculations using the full master equation showed that the Fokker-Planck equation substantially underestimated the strength of the features which emerge in the relative phase distribution in the quantum regime. Interestingly, a very similar underestimate of synchronization effects was obtained using a semiclassical model for the case of two van der Pol oscillators [7]. In our case, it seems that low photon occupation number is the key factor that leads to differences between quantum and semiclassical predictions.…”

“…Recent theoretical work has explored different ways of quantifying synchronization in quantum oscillators [5,7,14,15,20], as well as investigating the connection between it and measures of correlation such as mutual information and entanglement [5,8,10,15,19]. Detailed comparisons have also been made between the predictions of quantum models and those of related semiclassical or classical descriptions [7,12].…”

“…Studies of synchronization effects in the quantum regime have largely concentrated on the behavior of simple model systems such as van der Pol oscillators [7,9,10,12,15,17,19,21] (together with closely related models [22]), though a number of other systems including atomic ensembles [13,16] and optomechanical oscillators [5,6,12,18] have also been investigated. In this article we investigate synchronization in a very different model system consisting of two weakly coupled micromasers.…”

“…In the last few years there has been considerable interest in studying the synchronization of oscillators and related systems [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] close to threshold or at low excitation levels where semiclassical approaches break down and fully quantum mechanical calculations are required. Recent theoretical work has explored different ways of quantifying synchronization in quantum oscillators [5,7,14,15,20], as well as investigating the connection between it and measures of correlation such as mutual information and entanglement [5,8,10,15,19]. Detailed comparisons have also been made between the predictions of quantum models and those of related semiclassical or classical descriptions [7,12].…”

Synchronization in a semiclassical Kuramoto model

“…Initially, given the usual nature (scale) of the systems in which synchronization is typically observed, it seems superfluous thinking of a quantum theory for the Kuramoto model. However, there is not doubt about the fundamental importance of studying quantum fluctuations within the emergence of synchronized states [9][10][11][12][13][14][15][16]. Moreover, the Kuramoto model has been implemented on circuits and microand nanomechanical structures [17,18], systems that have already met the quantum domain [19,20].…”