Intermodulation in nonlinear SQUID metamaterials: Experiment and theory

Zhang, Daimeng; Trepanier, Melissa; Antonsen, Thomas M.; Ott, Edward; Anlage, Steven M.

doi:10.1103/physrevb.94.174507

Cited by 18 publications

(34 citation statements)

References 70 publications

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“…In unstable regions the perturbations λ i (t) show an exponential growth, while stability is assured, if only oscillatory solutions exist for λ i (t). The results agree with the general expectations [9,18,21], that those sections of ϕ a (ϕ dr ) are unstable, where the curve's slope is negative.…”

Section: A the Nonlinear Response Of Rf-squids To A Harmonic Drivingsupporting

confidence: 90%

“…Here, we study the resonant response of the metamaterial to a weak probe signal, while an additional strong driving (pump) signal pushes the metamaterial into a strongly nonlinear regime. In contrast to studies of intermodulation in SQUID metamaterials [18], where two signals of close frequencies induce sum and difference tones, here we consider signals with remote frequencies and are concerned with the strongly nonlinear behavior induced by the pump. The frequency of the pump is fixed, while the weak signal response is measured over a broad band of frequencies.…”

Section: Introductionmentioning

confidence: 99%

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Two-tone spectroscopy of a SQUID metamaterial in the nonlinear regime

Kiselev

Averkin

Fistul

et al. 2019

Phys. Rev. Research

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Compact microwave resonantors made of superconducting rings containing Josephson junctions (SQUIDs) are attractive candidates for building frequency tunable metamaterials with low losses and pronounced nonlinear properties. We explore the nonlinearity of a SQUID metamaterial by performing a two-tone resonant spectroscopy. The small-amplitude response of the metamaterial under strong driving by a microwave pump tone is investigated experimentally and theoretically. The transmission coefficient S21 of a weak probe signal is measured in the presence of the pump tone. Increasing the power of the pump, we observe pronounced oscillations of the SQUID's resonance frequency fres. The shape of these oscillations varies significantly with the frequency of the pump tone f dr . The response to the probe signal displays instabilities and sidebands. A state with strong second harmonic generation is observed. We provide a theoretical analysis of these observations, which is in good agreement with the experimental results.

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Section: A the Nonlinear Response Of Rf-squids To A Harmonic Drivingsupporting

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Two-tone spectroscopy of a SQUID metamaterial in the nonlinear regime

Kiselev

Averkin

Fistul

et al. 2019

Phys. Rev. Research

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“…More details on array fabrication, microwave design, global experimental characterization and rf simulation of similar rf-SQUIDs arrays has been described in Ref. 27,29,36,43 and Supp. Mat.…”

mentioning

confidence: 99%

Imaging collective behavior in an rf-SQUID metamaterial tuned by DC and RF magnetic fields

Zhuravel

Bae

Lukashenko

et al. 2019

Applied Physics Letters

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We examine the collective behavior of two-dimensional nonlinear superconducting metamaterials using a non-contact spatially resolved imaging technique. The metamaterial is made up of sub-wavelength nonlinear microwave oscillators in a strongly coupled 27×27 planar array of radio-frequency Superconducting QUantum Interference Devices (rf-SQUIDs). By using low-temperature laser scanning microscopy we image microwave currents in the driven SQUIDs while in non-radiating dark modes and identify the clustering and uniformity of like-oscillating meta-atoms. We follow the rearrangement of coherent patterns due to meta-atom resonant frequency tuning as a function of external dc and rf magnetic flux bias. We find that the rf current distribution across the SQUID array at zero dc flux and small rf flux reveals a low degree of coherence. By contrast, the spatial coherence improves dramatically upon increasing of rf flux amplitude, in agreement with simulation.Planar arrays of deep sub-wavelength dimension superconducting (SC) resonators have recently gained increasing attention due to their potential use as nonlinear metamaterials, i.e., engineered media whose electromagnetic response can differ dramatically from natural materials. Arrays of coupled SC resonators can be used for controllable routing and manipulating electromagnetic wave propagation in the range from radio-frequency (rf) 1,2 through the THz 3,4 domain. Demonstrated effects include electromagnetically 5 and self-induced broadband transparency, 6 negative magnetic permeability, 7 polarization rotation, 8 Fano resonance, 9 and multi-stable states. 10 Extensive progress on the development and applications of SC metamaterials has been achieved. 2,[11][12][13][14][15][16][17][18][19][20] It has been shown that such SC structures have significant advantages over their normal-metal counterparts allowing reduced losses by several orders of magnitude, shrinking the size of artificial meta-atoms, and achieving tunable frequency of operation by means of macroscopic quantum phenomena. 16,20 Traditional SC metamaterials are composed of ultracompact, self-resonating spirals and split-ring resonators (SRR) of different design. 1,15,16,18,21 Potentially, these structures could be used for switching, 5,10,22 as well as for tuning, by virtue of the dynamic range of well controllable manipulation of their resonances with external stimuli. 23,24 There has been great interest in using radio-frequency Superconducting QUantum Interference Devices: rf-SQUIDs as meta-atoms. 2,7,11,12,16,19,20,22,25,26 Contrary to the SRR and SC spiral, the rf-SQUID incorporates an extremely tunable nonlinear inductor, arising from the Josephson effect, when a Josephson junction is incorporated into a SC loop. The loop geometry adds the macroscopic quantum property of flux quantization, which in turn allows one to conveniently control the Josephson inductance through the magnetic flux applied to the loop. 27 The benefits of the rf-SQUID system were originally presented theoretically in the context of a...

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“…Under appropriate conditions, L JJ can controllably explore a variety of positive and negative values [20,21]. Josephson junctions have been used to create tunable and nonlinear magnetic metamaterials based mainly on radio frequency (rf) superconducting quantum interference devices (SQUIDs) [22][23][24][25][26][27][28]. Here we consider a complimentary electric metamaterial also tunable by means of the Josephson effect.…”

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confidence: 99%

Tunable superconducting Josephson dielectric metamaterial

et al. 2019

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We demonstrate a low-dissipation dielectric metamaterial with tunable properties based on the Josephson effect. Superconducting wires loaded with regularly spaced Josephson junctions (critical current Ic ≈ 0.25 µA) spanning a K-band waveguide and aligned with the microwave electric fields create a superconducting dielectric metamaterial. Applied dc current tunes the cutoff frequency and effective permittivity of this unique electric metamaterial. The results are in agreement with an analytical model for microwave transmission through the artificial dielectric medium.

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Intermodulation in nonlinear SQUID metamaterials: Experiment and theory

Cited by 18 publications

References 70 publications

Two-tone spectroscopy of a SQUID metamaterial in the nonlinear regime

Two-tone spectroscopy of a SQUID metamaterial in the nonlinear regime

Imaging collective behavior in an rf-SQUID metamaterial tuned by DC and RF magnetic fields

Tunable superconducting Josephson dielectric metamaterial

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