Quantum synchronization of two Van der Pol oscillators

Abstract

We study synchronization of two dissipatively coupled Van der Pol oscillators in the quantum regime. Due to quantum noise strict frequency locking is absent and is replaced by a crossover from weak to strong frequency entrainment. We discuss the differences to the behavior of one quantum Van der Pol oscillator subject to an external drive. Moreover, we describe a possible experimental realization of two coupled quantum van der Pol oscillators in an optomechanical setting.

Synchronization of micromasers

“…For dissipative coupling the master equation includes terms which describe an additional loss channel for the system whose properties depend on the state of both modes [10,12,17]…”

“…Synchronization has also been studied in quantum optical systems such as the laser, although generally focussing on regimes where approximate semiclassical descriptions work well [2,3]. 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].…”

“…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.…”

Observing quantum synchronization blockade in circuit quantum electrodynamics

“…when the limit cycle steady states of the oscillators are quantum states with no classical analog. Previous work on quantum synchronization has focused mainly on theoretically identifying and characterizing differences between classical and quantum synchronization [7][8][9][10][11][12][13][14][15][16][17][18] and on potential applications of the latter [19][20][21]. Experimental observation of quantum synchronization phenomena is hindered by the stringent requirements of high quantum coherence and strong nonlinearities, both of which are also key requirements for quantum computation.…”