Collective Dynamics in Optomechanical Arrays

Heinrich, Georg; Ludwig, Markus; Qian, J.; Kubala, Björn; Marquardt, Florian

doi:10.1103/physrevlett.107.043603

Cited by 398 publications

(404 citation statements)

References 36 publications

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“…Unlike our model, the mechanical resonators in Heinrich et al interact with a local electromagnetic field mode and are directly coupled by elastic forces. The more complex coupling in our model results in a different mechanism for the loss of synchronisation which typically occurs for large amplitude forcing not small amplitude forcing as occurs in the model of Heinrich et al [10]. Nevertheless we are able to give specific results on synchronisation for two and three mechanical resonators interacting via a common cavity mode and relate these to the behaviour of a collective variable, which is related to the cavity field amplitude.…”

Section: Introductionmentioning

confidence: 61%

“…This multi stable behaviour, resulting from the play off between weak damping and cavity forcing, has been noted elsewhere [8,10,24]. Here we explore it in more depth using amplitude equations.…”

Section: B Amplitude Equations and Multi-stability For Blue Detuningmentioning

confidence: 99%

“…More recently the collective dynamics of opto-mechanical arrays has been described by Heinrich et al [10], who give some results on synchronisation based on a phase model related to Kuramoto's model. Like our model, this paper is based on the radiation pressure coupling between the field and mechanical elements.…”

Section: Introductionmentioning

confidence: 99%

“…These intersect in a cusp bifurcation at δ = √ 3 and ǫ √ N Gω = 4ω √ 3 . The case ω = 2 is relevant for the experiments described in [8,10]. However for ω > 2, as in [22,23], there is no qualitative change in the bifurcation diagram, although the generalized Hopf bifurcation (δ = − 8ω 2 +3…”

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confidence: 99%

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Synchronization of many nanomechanical resonators coupled via a common cavity field

2012

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Using amplitude equations, we show that groups of identical nano-mechanical resonators, interacting with a common mode of a cavity microwave field, synchronize to form a single mechanical mode which couples to the cavity with a strength dependent on the square sum of the individual mechanical-microwave couplings. Classically this system is dominated by periodic behaviour which, when analyzed using amplitude equations, can be shown to exhibit multi-stability. In contrast groups of sufficiently dissimilar nano-mechanical oscillators may lose synchronization and oscillate out of phase at significantly higher amplitudes. Further the method by which synchronization is lost resembles that for large amplitude forcing which is not of the Kuramoto form.

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Section: Introductionmentioning

confidence: 61%

Section: B Amplitude Equations and Multi-stability For Blue Detuningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Synchronization of many nanomechanical resonators coupled via a common cavity field

2012

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“…Several experimental works have shown that synchronization can be observed in the laboratory within Josepshon junction arrays [40], nanomechanical systems [17], or optomechanical systems [41]. All of these systems share one prominent property: They behave quantum mechanically at sufficiently low temperatures.…”

Section: Discussionmentioning

confidence: 99%

Synchronization in a semiclassical Kuramoto model

et al. 2014

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Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards dynamical consensus has spurred a large body of theoretical and experimental research in recent decades. The Kuramoto model constitutes the most studied and paradigmatic framework in which to study synchronization. In particular, it shows how synchronization appears as a phase transition from a dynamically disordered state at some critical value for the coupling strength between the interacting units. The critical properties of the synchronization transition of this model have been widely studied and many variants of its formulations have been considered to address different physical realizations. However, the Kuramoto model has been studied only within the domain of classical dynamics, thus neglecting its applications for the study of quantum synchronization phenomena. Based on a system-bath approach and within the Feynman path-integral formalism, we derive equations for the Kuramoto model by taking into account the first quantum fluctuations. We also analyze its critical properties, the main result being the derivation of the value for the synchronization onset. This critical coupling increases its value as quantumness increases, as a consequence of the possibility of tunneling that quantum fluctuations provide.

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Mode Coupling in Electromechanical Systems: Recent Advances and Applications

Guo

Fang

Chen

et al. 2023

Adv Elect Materials

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Mode interactions have recently become the focus of intense research in micro/nanoelectromechanical systems (M/NEMS) due to their ability to improve device performance and explore the frontiers of fundamental physics. Understanding and controlling coupling between vibrational modes are critical for the development of advanced M/NEMS devices. This review summarizes the recent advances in studies of coupling between multiple modes in M/NEMS resonators, focusing especially on experimental developments and practical applications. First, depending on spatial distribution of interacting modes, this review divides the coupled mechanism in three types: intermode, near‐neighbor, and long‐range coupling. Then, several fundamental physics approaches based on mechanical‐mode coupling, including linear and nonlinear coupling, modal localization, synchronization, and phonon manipulation are reviewed. This review also introduces sensing applications by using coupled mechanical modes. Finally, the state‐of‐the‐art open questions and challenges are reviewed.

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Collective Dynamics in Optomechanical Arrays

Cited by 398 publications

References 36 publications

Synchronization of many nanomechanical resonators coupled via a common cavity field

Synchronization of many nanomechanical resonators coupled via a common cavity field

Synchronization in a semiclassical Kuramoto model

Mode Coupling in Electromechanical Systems: Recent Advances and Applications

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