Funding for Open Access provided by the UMD Libraries Open Access Publishing Fund.We have prepared meta-atoms based on radio-frequency superconducting quantum-interference devices (rf SQUIDs) and examined their tunability with dc magnetic field, rf current, and temperature. rf SQUIDs are superconducting split-ring resonators in which the usual capacitance is supplemented with a Josephson junction, which introduces strong nonlinearity in the rf properties. We find excellent agreement between the data and a model that regards the Josephson junction as the resistively and capacitively shunted junction. A magnetic field tunability of 80 THz=G at 12 GHz is observed, a total tunability of 56% is achieved, and a unique electromagnetically induced transparency feature at intermediate excitation powers is demonstrated for the first time. An rf SQUID metamaterial is shown to have qualitatively the same behavior as a single rf SQUID with regard to dc flux and temperature tuning.This work is supported by the NSF-GOALI Program through Grant No. ECCS-1158644 and the Center for Nanophysics and Advanced Materials (CNAM). Funding for Open Access was provided by the UMD Libraries Open Access Publishing Fund

Narrow-band invisibility in an otherwise opaque medium has been achieved by electromagnetically induced transparency (EIT) in atomic systems. The quantum EIT behavior can be classically mimicked by specially engineered metamaterials via carefully controlled interference with a "dark mode." However, the narrow transparency window limits the potential applications that require a tunable wideband transparent performance. Here, we present a macroscopic quantum superconducting metamaterial with manipulative self-induced broadband transparency due to a qualitatively novel nonlinear mechanism that is different from conventional EIT or its classical analogs. A near-complete disappearance of resonant absorption under a range of applied rf flux is observed experimentally and explained theoretically. The transparency comes from the intrinsic bistability of the meta-atoms and can be tuned on and off easily by altering rf and dc magnetic fields, temperature, and history. Hysteretic in situ 100% tunability of transparency paves the way for autocloaking metamaterials, intensity-dependent filters, and fast-tunable power limiters.

The response of nonlinear metamaterials and superconducting electronics to two-tone excitation is critical for understanding their use as low-noise amplifiers and tunable filters. A new setting for such studies is that of metamaterials made of radio frequency superconducting quantum interference devices (rf-SQUIDs). The two-tone response of self-resonant rf-SQUID meta-atoms and metamaterials is studied here via intermodulation (IM) measurement over a broad range of tone frequencies and tone powers. A sharp onset followed by a surprising strongly suppressed IM region near the resonance is observed. Using a two time scale analysis technique, we present an analytical theory that successfully explains our experimental observations. The theory predicts that the IM can be manipulated with tone power, center frequency, frequency difference between the two tones, and temperature. This quantitative understanding potentially allows for the design of rf-SQUID metamaterials with either very low or very high IM response.

Through experiments and numerical simulations we explore the behavior of rf SQUID (radio frequency superconducting quantum interference device) metamaterials, which show extreme tunability and nonlinearity. The emergent electromagnetic properties of this metamaterial are sensitive to the degree of coherent response of the driven interacting SQUIDs. Coherence suffers in the presence of disorder, which is experimentally found to be mainly due to a dc flux gradient. We demonstrate methods to recover the coherence, specifically by varying the coupling between the SQUID meta-atoms and increasing the temperature or the amplitude of the applied rf flux.Metamaterials are artificially structured media with electromagnetic properties arising from the structure of individual meta-atoms and the interactions between them. Metamaterials can have emergent properties not seen in natural materials e.g. a negative index of refraction [1-3], cloaking [4,5], and super-resolution imaging [6,7]. Collections of superconducting split ring resonators (SRRs) have an effective permeability that can be tuned by suppressing superconductivity with increased temperature and applied magnetic field [8-11], or applied current [12]. Suppressing superconductivity tunes the kinetic inductance but this process increases losses and can be slow.The rf SQUID, which has a Josephson junction instead of the capacitive gap, is a significant improvement over the SRR; by applying a magnetic field the self-resonance can be tuned quickly over a wide range without a substantial increase in losses [13]. Using an rf SQUID as a meta-atom was proposed theoretically [14][15][16] and experimentally demonstrated [13,17]. Previous experimental work on rf SQUID array metamaterials has been limited to 1D arrays [18][19][20] and theoretical work has only considered nearest neighbor coupling between the SQUIDs. [21][22][23][24][25]. In this paper, we consider dense globally coupled 2D arrays and study the behavior resulting from the complex interactions between the SQUIDs, not seen in a 1D configuration.One of the challenges of nonlinear metamaterials is understanding and controlling their collective behavior, which is not a simple linear superposition of the response of each meta-atom. An rf SQUID metamaterial is an array of driven linearly-coupled nonlinear oscillators [26]. The Kuramoto model has been used to study coherence in related systems, such as 1D arrays of current-biased Josephson junctions [27][28][29]. The typical Kuramoto system is a collection of linear harmonic oscillators with a Gaussian distribution of self-resonant frequencies. These oscillators interact through nonlinear uniform all-to-all coupling. Under certain conditions the entire array can oscillate in phase at the same frequency (coherence), despite the differences in self-resonant frequencies.The Kuramoto model quantifies coherence with an order parameter, r = 1 N N j e iθj where θ j is the phase of the jth oscillator and N is the number of oscillators. Perfect coherence (r = 1) is achieved when...

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.