Quantum signatures of chimera states

Abstract

Chimera states are complex spatiotemporal patterns in networks of identical oscillators, characterized by the coexistence of synchronized and desynchronized dynamics. Here we propose to extend the phenomenon of chimera states to the quantum regime, and uncover intriguing quantum signatures of these states. We calculate the quantum fluctuations about semiclassical trajectories and demonstrate that chimera states in the quantum regime can be characterized by bosonic squeezing, weighted quantum correlations, and measures of mutual information. Our findings reveal the relation of chimera states to quantum information theory, and give promising directions for experimental realization of chimera states in quantum systems.PACS numbers: 05.45. Xt,05.30.Rt, 42.50.Lc, 42.65.Sf In classical systems of coupled nonlinear oscillators, the phenomenon of chimera states, which describes the spontaneous emergence of coexisting synchronized and desynchronized dynamics in networks of identical elements, has recently aroused much interest [1]. These intriguing spatio-temporal patterns were originally discovered in models of coupled phase oscillators. In this case, they exist due to nonlocal coupling between identical elements of the ensemble [2, 3]. There has been extensive work on the theoretical investigation of chimera states [4][5][6][7][8][9][10][11][12][13][14][15][16] While synchronization of classical oscillators has been well studied since the early observations of Huygens in the 17th century [26], synchronization in quantum mechanics has only very recently become a focus of interest. For example, quantum signatures of synchronization in a network of globally coupled Van der Pol oscillators have been investigated [27,28]. Related works focus on the dynamical phase transitions of a network of nanomechanical oscillators with arbitrary topologies characterized by a coordination number [29], and the semiclassical quantization of the Kuramoto model by using path integral methods [30].Contrary to classical mechanics, in quantum mechanics the notion of phase-space trajectory is not well defined. As a consequence, one has to define new measures of synchronization for continuous variable systems like optomechanical arrays [29]. These measures are based on quadratures of the coupled systems and allow one to extend the notion of phase synchronization to the quantum regime [31] [35,36], and mutual information [37]. Despite the intensive theoretical investigation of quantum signatures of synchronized states, to date, studies of the quantum manifestations of chimera states are still lacking.In this Letter we study the emergence of chimera states in a network of coupled quantum Van der Pol oscillators. Unlike in previous work [38], we address here the fundamental issue of the dynamical properties of chimera states in a continuous variable system. Considering the chaotic nature of chimera states [11], we study the shorttime evolution of the quantum fluctuations at the Gaussian level. This approach allows us to use powerful tools of quan...

Synchronization of micromasers

“…Recent work on coupled quantum van der Pol oscillators has suggested that there may be an intimate connection between the emergence of synchronization in coupled quantum oscillators and the behavior of the mutual information [8,15,19] and it has even been suggested that mutual information could serve as an order parameter for synchronization [15].…”

“…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].…”

Chimera states in coupled Kuramoto oscillators with inertia

“…This so-called chimera state is counter-intuitive as it appears even when the oscillators are identical, but, since its discover, this state has become a relevant subject of investigation for experimental and theoretical scientists active in different fields ranging from laser dynamics to chemical oscillators, from mechanical pendula to (computational) neuroscience. In particular chimera states have been shown to emerge in various numerical/theoretical studies [26][27][28][29][30][31][32][33][34][35] and in various experimental settings, including mechanical [36][37][38], (electro-)chemical [39][40][41] lasing systems [42,43] and BOLD fMRI signals detection during resting state activity [44], among others. Therefore chimera states are an ubiquitous phenomenon in nature much like synchronization itself and may often have been overlooked or dismissed in previous studies.…”

Does hyperbolicity impede emergence of chimera states in networks of nonlocally coupled chaotic oscillators?

“…They represent an intriguing phenomenon where an ensemble of identical elements with symmetric coupling spontaneously splits into spatially separated coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics. Since their first discovery in systems of coupled phase oscillators [2,3] they have been found in a broad range of diverse models [1,4], ranging from time-discrete maps [5] and time-continuous chaotic models [6], Stuart-Landau oscillators [7][8][9][10], globally coupled lasers [11], Van der Pol oscillators [12,13] FitzHugh-Nagumo neural systems [14,15], population dynamical models [16] to autonomous Boolean networks [17]. They have recently also been observed experimentally, e.g., in optical light modulators [18], chemical [19], mechanical [20,21], electronic [22,23], optoelectronic [24], and electrochemical [25,26] oscillator systems.…”