Susanne Butz

Low-loss tunable metamaterials using superconducting circuits with Josephson junctions

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.

Multistability and switching in a superconducting metamaterial

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 meta-atoms. 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.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 by creating sub-wavelength lattices of electronic or plasmonic structures, so-called meta-atoms, that determine the interaction between light and metamaterial. One of the ultimate goals for these tailored media is the ability to control their properties in-situ which has led to a whole new branch of tunable and switchable metamaterials.1–4 Many of the present realizations rely on introducing microelectromechanical actuators or semiconductor elements into their meta-atom structures.3 Here we show that superconducting quantum interference devices (SQUIDs) can be used as fast, intrinsically switchable meta-atoms. We found 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 a nanosecond long pulse in addition to the microwave probe signal. Apart from potential applications such as, for example, an all-optical metamaterial switch, these results suggest that multi-stability, which is a common feature in many nonlinear systems, can be utilized to create new types of meta-atoms.

A one-dimensional tunable magnetic metamaterial

We present experimental data on a one-dimensional super-conducting 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 μr,eff from the measured data, we employ a technique that uses only the complex transmission coefficient S₂₁.

Protecting SQUID metamaterials against stray magnetic fields

Using superconducting quantum interference devices (SQUIDs) as the basic, low-loss elements of thin-film metamaterials has one main advantage: their resonance frequency is easily tunable by applying a weak magnetic field. The downside, however, is a strong sensitivity to stray and inhomogeneous magnetic fields. In this work, we demonstrate that even small magnetic fields from electronic components destroy the collective, resonant behaviour of the SQUID metamaterial. We also show how the effect of these fields can be minimized. As a first step, magnetic shielding decreases any initially present fields, including the earth’s magnetic field. However, further measures such as improvements in the sample geometry have to be taken to avoid the trapping of Abrikosov vortices.

Design and experimental study of superconducting left-handed transmission lines with tunable dispersion

We study the microwave properties of a superconducting tunable coplanar waveguide (CPW). Pairs of Josephson junctions are forming superconducting quantum interference devices (SQUIDs), which shunt the central conductor of the CPW. The Josephson inductance of the SQUIDs is varied in the range of 0.08‐0.5 nH by applying a dc magnetic field. The central conductor of the CPW contains Josephson junctions connected in series that provide extra inductances; the magnetic field controlling the SQUIDs is weak enough not to influence the inductance of the chain of the single junctions. The circuit is designed to have left- and right-handed transmission properties separated by a variable rejection band; the band edges can be tuned by the magnetic field. We present transmission measurements on CPWs based on up to 120 Nb‐AlOx‐Nb Josephson junctions. At zero magnetic field, we observed no rejection band in the frequency range of 8‐11 GHz. When applying the magnetic field, a rejection band between 7 GHz and 9 GHz appears. The experimental data are compared with numerical simulations. (Some figures may appear in colour only in the online journal)

A one-dimensional tunable magnetic metamaterial: erratum

We have detected an error in our data retrieval script which prepares the measured transmission data for the conversion to magnetic permeability. Correcting this error requires modification of Fig. 4(b) and Fig. 5 in the original publication. All methods, calculations and the conclusion in the published paper are still correct.

Magnetically induced transparency of a quantum metamaterial composed of twin flux qubits

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.Here, the authors demonstrate an array of superconducting qubits embedded into a microwave transmission line. They show that the transmission through the metamaterial periodically depends on externally applied magnetic field and suppression of the transmission is achieved through field-induced transitions.

Coherent oscillations of driven rf SQUID metamaterials

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.