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arXiv:1808.05047 · New Journal of Physics

Dynamics of many-body quantum synchronisation

Claire Davis-Tilley, C K Teoh, Andrew D. Armour

Published Oct 18, 2018• 28 citations
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Abstract

We analyse the properties of the synchronisation transition in a many-body system consisting of quantum van der Pol oscillators with all-to-all coupling using a self-consistent mean-field method. We find that the synchronised state, which the system can access for oscillator couplings above a critical value, is characterised not just by a lower phase uncertainty than the corresponding unsynchronised state, but also a higher number uncertainty. Just below the critical coupling the system can evolve to the unsynchronised steady state via a long-lived transient synchronised state. We investigate the way in which this transient state eventually decays and show that the critical scaling of its lifetime is consistent with a simple classical model.

DOI
10.1088/1367-2630/aae947

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We analyse the properties of the synchronisation transition in a many-body system consisting of quantum van der Pol oscillators with all-to-all coupling using a self-consistent mean-field method. We find that the synchronised state, which the system can access for oscillator couplings above a critical value, is characterised not just by a lower phase uncertainty than the corresponding unsynchronised state, but also a higher number uncertainty. Just below the critical coupling the system can evolve to the unsynchronised steady state via a long-lived transient synchronised state. We investigate the way in which this transient state eventually decays and show that the critical scaling of its lifetime is consistent with a simple classical model.
Synchronisation has been explored extensively for classical systems from the mid-1600s, and is a phenomenon widely understood in many diverse systems. In the age of technology miniaturisation, there are great incentives to develop an understanding of quantum synchronisation, where quantum fluctuations become the dominant source of noise and non-classical features become important. This thesis considers different types of synchronisation in systems that can display highly non-linear, quantum behaviours. Phase synchronisation for a micromaser coupled to an external drive is initially considered, and it is found that for low photon numbers a semiclassical approximation underestimates phase synchronisation, but a perturbation theory can be accurate for sufficiently weak coupling in either a quantum or semiclassical regime. When a small detuning between the drive and micromaser is introduced, frequency entrainment is also found to exist. Then two micromasers are coupled with each other, in two different configurations, and synchronisation through a relative phase preference is found for each. A semiclassical approximation once again underestimates the phase synchronisation. Entanglement and mutual information are found to behave differently to the relative phase preference depending on each system's parameters. Finally, a mean-field theory is considered for many coupled van der Pol oscillators and micromasers respectively. As the coupling between the oscillators is increased, a critical point is reached and the systems undergo a transition to a phase synchronised state. This bistability appears via a saddle-node bifurcation, and in addition to examining a variety of properties before and after the transition the critical scaling behaviour was investigated close to the transition.
Quantum van der Pol oscillators are driven-dissipative systems displaying quantum synchronization phenomena. When forced by a squeezed drive, the frequency adjusts to half of the forcing displaying multiple preferred phases. Here we analyze the physical origin of this entrained response, establishing a connection with metastability in open quantum systems. We report a dynamical regime characterized by a huge separation of time scales, in which a dynamical mode displays a lifetime that can be orders of magnitude larger than the rest. In this regime, the long-time dynamics is captured by an incoherent process between two metastable states, which correspond to the preferred phases of the synchronized oscillator. In fact, we show that quantum entrainment is here characterized by fluctuations driving an incoherent process between two metastable phases, which ultimately limits its temporal coherence when moving into the quantum regime. Finally, we discuss connections with the phenomena of dissipative phase transitions and transient synchronization in open quantum systems.
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We employ a quantum trajectory approach to characterize synchronization and phase-locking between open quantum systems in nonequilibrium steady states. We exemplify our proposal for the paradigmatic case of two quantum Van der Pol oscillators interacting through dissipative coupling. \nWe show the deep impact of synchronization on the statistics of phase-locking indicators and other correlation measures defined for single trajectories, spotting a link between the presence of synchronization and the emergence of large tails in the probability distribution for the entanglement along trajectories. Our results shed new light on fundamental issues regarding quantum synchronization providing new methods for its precise quantification.