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arXiv:2006.13623 · Physical Review Research

Generalized measure of quantum synchronization

Noufal Jaseem, Michal Hajdušek, Parvinder Solanki, L. C. Kwek, Rosario Fazio, Sai Vinjanampathy

Published Nov 30, 2020• 58 citations
arXivHTMLPDF

Abstract

We present a generalized information-theoretic measure of synchronization in quantum systems.This measure is applicable to dynamics of anharmonic oscillators, few-level atoms, and coupled oscillator networks.Furthermore, the new measure allows us to discuss synchronization of disparate physical systems such as coupled hybrid quantum systems and coupled systems undergoing mutual synchronization that are also driven locally.In many cases of interest, we find a closed-form expression for the proposed measure.

DOI
10.1103/physrevresearch.2.043287

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We present a generalized information-theoretic measure of synchronization in quantum systems.This measure is applicable to dynamics of anharmonic oscillators, few-level atoms, and coupled oscillator networks.Furthermore, the new measure allows us to discuss synchronization of disparate physical systems such as coupled hybrid quantum systems and coupled systems undergoing mutual synchronization that are also driven locally.In many cases of interest, we find a closed-form expression for the proposed measure.
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We introduce and characterize two different measures which quantify the level of synchronization of coupled continuous variable quantum systems. The two measures allow us to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is, in principle, unbounded; however, in the absence of quantum resources (e.g., squeezing) the synchronization level is bounded below a certain threshold. We elucidate some interesting connections between entanglement and synchronization and, finally, discuss an application based on quantum optomechanical systems.
We introduce the concept of degree of quantumness in quantum synchronization, a measure of the quantum nature of synchronization in quantum systems. Following techniques from quantum information, we propose the number of non-commuting observables that synchronize as a measure of quantumness. This figure of merit is compatible with already existing synchronization measurements, and it captures different physical properties. We illustrate it in a quantum system consisting of two weakly interacting cavity-qubit systems, which are coupled via the exchange of bosonic excitations between the cavities. Moreover, we study the synchronization of the expectation values of the Pauli operators and we propose a feasible superconducting circuit setup. Finally, we discuss the degree of quantumness in the synchronization between two quantum van der Pol oscillators.
Natural and engineered classical systems are replete with examples of synchronization, understood as the adjustment of rhythms of physical systems. Such synchronization is at the heart of the stability of several classical technologies, such as mechanical bridges and electrical networks. Given the advent of quantum simulation and computation technologies, it is natural to study a quantum analogue of synchronization and explore novel applications. This review surveys synchronization in few and many-body quantum systems, measures that quantify them, and their applications to quantum technologies.
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