We report on experiments with superconducting metamaterials containing Josephson junctions. In these structures, split-ring resonators used in conventional metamaterials are replaced by superconducting loops that are interrupted by Josephson junctions, so called rf-SQUIDs. Like the split-ring resonators, these elements can be seen as LC-resonators that couple to the magnetic field. The advantage of superconducting thin-film metamaterials is that, due to the tunable intrinsic inductance of the Josephson junction, the resonance frequency of the rf-SQUID can be changed by applying an external dc magnetic field. We present experimental results that demonstrate the tunability of the resonance frequency of these devices.
The field of metamaterial research revolves around the idea of creating artificial media that interact with light in a way unknown from naturally occurring materials. This is commonly achieved using sub-wavelength lattices of electronic or plasmonic structures, so-called metaatoms. One of the ultimate goals for these tailored media is the ability to control their properties in situ. Here we show that superconducting quantum interference devices can be used as fast, switchable meta-atoms. We find that their intrinsic nonlinearity leads to simultaneously stable dynamic states, each of which is associated with a different value and sign of the magnetic susceptibility in the microwave domain. Moreover, we demonstrate that it is possible to switch between these states by applying nanosecond-long pulses in addition to the microwave-probe signal. Apart from potential applications for this all-optical metamaterial switch, the results suggest that multistability can also be utilized in other types of nonlinear meta-atoms.
Abstract:We present experimental data on a one-dimensional superconducting metamaterial that is tunable over a broad frequency band. The basic building block of this magnetic thin-film medium is a single-junction (rf-) superconducting quantum interference device (SQUID). Due to the nonlinear inductance of such an element, its resonance frequency is tunable in situ by applying a dc magnetic field. We demonstrate that this results in tunable effective parameters of our metamaterial consisting of 54 rf-SQUIDs. In order to obtain the effective magnetic permeability µ r,eff from the measured data, we employ a technique that uses only the complex transmission coefficient S 21 .
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...
Quantum theory is expected to govern the electromagnetic properties of a quantum metamaterial, an artificially fabricated medium composed of many quantum objects acting as artificial atoms. Propagation of electromagnetic waves through such a medium is accompanied by excitations of intrinsic quantum transitions within individual meta-atoms and modes corresponding to the interactions between them. Here we demonstrate an experiment in which an array of double-loop type superconducting flux qubits is embedded into a microwave transmission line. We observe that in a broad frequency range the transmission coefficient through the metamaterial periodically depends on externally applied magnetic field. Field-controlled switching of the ground state of the meta-atoms induces a large suppression of the transmission. Moreover, the excitation of meta-atoms in the array leads to a large resonant enhancement of the transmission. We anticipate possible applications of the observed frequency-tunable transparency in superconducting quantum networks.
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