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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Synchronization and quantum correlations in harmonic networks

Gonzalo Manzano, Fernando Galve, Gian Luca Giorgi, Pere Colet, Emilio Hernández-Garcı́a, Roberta Zambrini

Published May 1, 2013• 0 citations
Publisher

Abstract

Synchronization phenomena have been observed in a broad range of physical, chemical and biological systems but there are few attempts to describe them in the quantum regime. Most of the attention in this regime has been devoted to the problem of entrainment induced by an external driving [1] and not to spontaneous synchronization. We also mention recent research by different groups on synchronization of nano/microscopic systems [2]. Even if these works [2] are concerned with classical (average) properties, such optomechanical devices are indeed susceptible of having quantum behaviour, being the subject of an intense experimental effort. In [3], for the first time, we established the connections between the phenomenon of synchronization and quantum correlations.

DOI
10.1109/cleoe-iqec.2013.6801691

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Synchronization phenomena have been observed in a broad range of physical, chemical and biological systems but there are few attempts to describe them in the quantum regime. Most of the attention in this regime has been devoted to the problem of entrainment induced by an external driving [1] and not to spontaneous synchronization. We also mention recent research by different groups on synchronization of nano/microscopic systems [2]. Even if these works [2] are concerned with classical (average) properties, such optomechanical devices are indeed susceptible of having quantum behaviour, being the subject of an intense experimental effort. In [3], for the first time, we established the connections between the phenomenon of synchronization and quantum correlations.
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although several mechanisms and conditions for synchronous behavior in spatially extended systems and networks have been identified, the emergence of this phenomenon has been largely unexplored in quantum systems until very recently. Here we discuss synchronization in quantum networks of different harmonic oscillators relaxing towards a stationary state, being essential the form of dissipation. By local tuning of one of the oscillators, we establish the conditions for synchronous dynamics, in the whole network or in a motif. Beyond the classical regime we show that synchronization between (even unlinked) nodes witnesses the presence of quantum correlations and entanglement. Furthermore, synchronization and entanglement can be induced between two different oscillators if properly linked to a random network.
Can synchronization -- the widespread spontaneous emergence of coordinated dynamics in classical nonlinear systems -- also occur in the quantum regime? This question has recently sparked intense research into collective behavior and temporal self-organization in quantum systems. Typical quantum features such as the linearity of time evolution and the presence of quantum noise seem to hinder the appearance of synchrony at the microscopic level. At the same time, quantum coherence and quantum correlations may provide novel mechanisms for enhancing synchronization beyond its classical counterpart. We here survey recent theoretical and experimental advances in quantum synchronization, ranging from the characterization of synchronous oscillations and genuinely nonclassical forms of synchrony to many-body synchronization on quantum networks.
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.
The emergence of mutual synchronization between oscillators, largely studied in classical systems, is explored in quantum systems. After reviewing recent research about the quantum aspects of this phenomenon, we present results obtained in the case of coupled harmonic oscillators with different natural frequencies. The presence of different dissipation processes, described by common or separate heat baths, plays a crucial role in the dynamical properties of the system. We show that mutual synchronization phenomena may appear only for a common bath. Furthermore we show that the emergence of synchronization is related to robust quantum correlations between the oscillators. Synchronization phenomena appear indeed in correspondence with large plateau where mutual information and quantum discord decay slowly, showing for the first time a quantum feature of spontaneous synchronization.
The phenomenon of spontaneous synchronization arises in a broad range of systems when the mutual interaction strength among components overcomes the effect of detuning. Recently it has been studied also in the quantum regime with a variety of approaches and in different dynamical contexts. We review here transient synchronization arising during the relaxation of open quantum systems, describing the common enabling mechanism in presence of either local or global dissipation. We address both networks of harmonic oscillators and spins and compare different synchronization measures.
We show the emergence of spontaneous synchronization between a pair of detuned quantum oscillators within a harmonic network. Our model does not involve any nonlinearity, driving, or external dissipation, thus providing the simplest scenario for the occurrence of local coherent dynamics in an extended harmonic system. A sufficient condition for synchronization is established by building upon the Rayleigh normal mode approach to vibrational systems. Our results show that mechanisms favoring synchronization, even between oscillators that are not directly coupled to each other, are transient energy depletion and crosstalk. We also address the possible buildup of quantum correlations during synchronization and show that indeed entanglement may be generated in detuned systems, starting from uncorrelated states and without any direct coupling between the two oscillators.