Novel self-sustained modulation in superconducting stripline resonators

Segev, Eran; Abdo, Baleegh; Shtempluck, Oleg; Buks, Eyal

doi:10.1209/0295-5075/78/57002

Cited by 13 publications

(20 citation statements)

References 22 publications

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“…The superconducting resonator model developed in [1,11,12,13] is intriguing to study from the point of view of the still young bifurcation theory of piecewisesmooth systems. Moreover, it is vital to reliable operation of the physical device that the cause of self-sustaining oscillations is identified, that the parameters for which they and other attractors exist are found.…”

Section: Discussionmentioning

confidence: 99%

“…The microbridge sits around the circumference of a conducting ring attached to a sensor probe. In experiment, however, novel self-sustaining oscillations are observed [1,11,12,13]. They have a simple physical origin, namely the oscillation of the microbridge between normal and superconducting states: at a low temperature the microbridge is superconducting, passing a high current which heats the bridge, until its temperature exceeds the threshold where it ceases to be superconducting, the conductance falls, the current therefore decreases and the heating effect drops, so the bridge temperature falls below the threshold, the bridge becomes superconducting, and the process is seen to repeat periodically.…”

Section: Piecewise-smooth Model Of a Superconducting Resonatormentioning

confidence: 95%

“…[3,5]. In this paper we study the piecewise smooth model of a superconducting resonator, derived in [1,11,12,13] to explain the appearance of novel self-sustaining oscillations, to show how an attractor is created, and the oscillations destroyed, via a sequence of discontinuity-induced bifurcations whose theory that are novel from both theoretical and experimental perspectives.…”

Section: Introductionmentioning

confidence: 99%

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Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator

Jeffrey

2012

Physica D: Nonlinear Phenomena

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Jeffrey, M. R. (2012). Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator. University of Bristol -Explore Bristol Research General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator Mike R. Jeffrey 1 AbstractThe nonsmooth dynamical model of a superconducting resonator is discussed, based on previous experimental and analytical studies. The device is a superconducting sensor whose key elements are a sensor probe attached to a conducting ring, around which flows an electric current. The ring is interrupted by a microbridge of superconducting material, whose temperature can be altered to sensitively control the device's conductivity. In certain conditions, novel self-sustaining power oscillations are observed, and can suddenly disappear. It was previously shown that this disappearance can be described by a periodic attractor undergoing a catastrophic sliding bifurcation. Here we reveal the sequence of bifurcations that leads up to this event, beginning with the change in stability of a fixed point that creates an attractor, and the birth of a saddle-type periodic orbit by means of a Hopf-like discontinuity-induced bifurcation.

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Section: Discussionmentioning

confidence: 99%

Section: Piecewise-smooth Model Of a Superconducting Resonatormentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator

Jeffrey

2012

Physica D: Nonlinear Phenomena

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“…They occur in singular perturbation problems such as the van der Pol system with relation to canards and relaxation oscillations [5,12,18], where the sliding vector field is comparable to the 'reduced' (or slow) subsystem. They have also been proposed as the mechanism for sudden temperature oscillations observed in superconducting resonators [15,25], and have been shown to be generic in switched feedback controllers [4].…”

Section: Completeness Of the Classificationmentioning

confidence: 99%

The Geometry of Generic Sliding Bifurcations

Jeffrey¹,

Hogan²

2011

SIAM Rev.

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Abstract. Using the singularity theory of scalar functions, we derive a classification of sliding bifurcations in piecewise-smooth flows. These are global bifurcations which occur when distinguished orbits become tangent to surfaces of discontinuity, called switching manifolds. The key idea of the paper is to attribute sliding bifurcations to singularities in the manifold's projection along the flow, namely to points where the projection contains folds, cusps, and two-folds (saddles and bowls). From the possible local configurations of orbits we obtain sliding bifurcations.In this way we derive a complete classification of generic one-parameter sliding bifurcations at a smooth codimension one switching manifold in n-dimensions for n ≥ 3. We uncover previously unknown sliding bifurcations, all of which are catastrophic in nature. We also describe how the method can be extended to sliding bifurcations of codimension two or higher.Key words. Sliding, Filippov, discontinuity, bifurcation, singularity, grazing AMS subject classifications. 34C23,37G05,37G10,37G151. Introduction. Bifurcation theory for systems of ordinary differential equations describes how smooth variations of parameter values can, through topological changes, cause sudden changes in dynamics. This paper considers the effect of discontinuous variation in the differential equations themselves, which give rise to the discontinuity-induced bifurcations [6] of piecewise-smooth dynamical systems.We will study bifurcations that affect individual orbits as a single parameter varies. The Flowbox Theorem [23] shows that in the neighbourhood U of a point where a flow is smooth and non-vanishing, all orbits are smoothly equivalent. We cannot, therefore, study the global bifurcation of a distinguished orbit Γ passing through U by studying dynamics in U alone. The same is not true if the flow is piecewisesmooth in U with a discontinuity along a surface Σ. Then parameter variation can lead to local changes in the intersection between Γ and Σ. If the change involves orbits which are confined to 'slide' along the discontinuity then this is called a sliding bifurcation. Provided that the discontinuity occurs along a smooth codimension one switching manifold, we will show that all one parameter sliding bifurcations in R n are equivalent to just 8 cases, each of which occur generically in R 2 or R 3 , and of which only four are already known.Piecewise-smooth systems are widespread in applications such as engineering, economics, medicine, biology and ecology. Problems with impacts, friction, or switching are piecewise-smooth. For recent accounts of such systems see [6,21,34]. The systems we consider are expressible in the forṁ

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“…In our previous studies, we have investigated several effects, e.g., strong amplification, 13 noise squeezing, 13 and response to optical illumination, 14,15 which occur near this bifurcation, and limit cycle oscillations, which are observed in the astable zone. 16,17 In the present work, we investigate experimentally and theoretically the response of the system to an amplitude modulated input signal and find an unusual SR mechanism that has both properties of extremely strong responsivity and nonhysteretic behavior. The frequency bandwidth of this mechanism is found to be limited by the rate of thermal relaxation.…”

mentioning

confidence: 93%

Stochastic resonance with a single metastable state: Thermal instability in NbN superconducting stripline resonators

et al. 2008

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We study thermal instability in NbN superconducting stripline resonators. The system exhibits extreme nonlinearity near a bifurcation, which separates a monostable zone and an astable one. The lifetime of the metastable state, which is locally stable in the monostable zone, is measured near the bifurcation and the results are compared with a theory. Near bifurcation, where the lifetime becomes relatively short, the system exhibits strong amplification of a weak input modulation signal. We find that the frequency bandwidth of this amplification mechanism is limited by the rate of thermal relaxation. When the frequency of the input modulation signal becomes comparable or larger than this rate, the response of the system exhibits subharmonics of various orders.Stochastic resonance ͑SR͒ is a phenomenon in which metastability in nonlinear systems is exploited to achieve amplification of weak signals. 1-3 SR has been experimentally demonstrated in electrical, optical, superconducting, neuronal, and mechanical systems. 4-12 Usually, SR is achieved by operating the system in a region in which it has two metastable states and its response exhibits hysteresis. Under some appropriate conditions, a weak input signal, which modulates the transition rates between these states, can lead to synchronized noise-induced transitions, thus allowing strong amplification.In this Brief Report, we investigate SR and amplification in a superconducting ͑SC͒ NbN stripline resonator. Contrary to previous studies, we operate the system near a bifurcation between a monostable zone, in which the system has a single metastable state, and an astable zone, in which this state ceases to exist and the system lacks any steady states. In our previous studies, we have investigated several effects, e.g., strong amplification, 13 noise squeezing, 13 and response to optical illumination, 14,15 which occur near this bifurcation, and limit cycle oscillations, which are observed in the astable zone. 16,17 In the present work, we investigate experimentally and theoretically the response of the system to an amplitude modulated input signal and find an unusual SR mechanism that has both properties of extremely strong responsivity and nonhysteretic behavior. The frequency bandwidth of this mechanism is found to be limited by the rate of thermal relaxation. We find that rather unique subharmonics of various orders are generated when the modulation frequency becomes comparable or larger than the relaxation rate. Moreover, we measure the lifetime of the metastable state in the monostable zone near the bifurcation and compare the results with a theory.Our experiments are performed using a device that integrates a narrow microbridge into a SC stripline electromagnetic resonator. Design considerations, fabrication details, as well as resonance modes calculation can be found elsewhere. 14 The dynamics of our system can be captured by two coupled equations of motion, which are hereby briefly described ͑see Ref. 17 for a detailed derivation͒. Consider a resonator driven ...

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Novel self-sustained modulation in superconducting stripline resonators

Cited by 13 publications

References 22 publications

Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator

Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator

The Geometry of Generic Sliding Bifurcations

Stochastic resonance with a single metastable state: Thermal instability in NbN superconducting stripline resonators

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