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arXiv:1505.00385 · Physical Review B

Mode engineering with a one-dimensional superconducting metamaterial

Masahiko Taguchi, D. M. Basko, F. W. J. Hekking

Published Jul 10, 2015• 13 citations
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Abstract

We propose a way to control the Josephson energy of a single Josephson junction embedded in a one-dimensional superconducting metamaterial: an inhomogeneous superconducting loop, made out of a superconducting nanowire or a chain of Josephson junctions. The Josephson energy is renormalized by the electromagnetic modes propagating along the loop. We study the behavior of the modes as well as of their frequency spectrum when the capacitance and the inductance along the loop are spatially modulated. We show that, depending on the amplitude of the modulation, the renormalized Josephson energy is either larger or smaller than the one found for a homogeneous loop. Using typical experimental parameters for Josephson junction chains and superconducting nanowires, we conclude that this mode engineering can be achieved with currently available metamaterials.

DOI
10.1103/physrevb.92.024507

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We propose a way to control the Josephson energy of a single Josephson junction embedded in a one-dimensional superconducting metamaterial: an inhomogeneous superconducting loop, made out of a superconducting nanowire or a chain of Josephson junctions. The Josephson energy is renormalized by the electromagnetic modes propagating along the loop. We study the behavior of the modes as well as of their frequency spectrum when the capacitance and the inductance along the loop are spatially modulated. We show that, depending on the amplitude of the modulation, the renormalized Josephson energy is either larger or smaller than the one found for a homogeneous loop. Using typical experimental parameters for Josephson junction chains and superconducting nanowires, we conclude that this mode engineering can be achieved with currently available metamaterials.
We report a theoretical study of the low-frequency impedance of a Josephson junction chain whose parameters vary in space. Our goal is to find the optimal spatial profile which maximizes the total inductance of the chain without shrinking the low-frequency window where the chain behaves as an inductor. If the spatial modulation is introduced by varying the junction areas, we find that the best result is obtained for a spatially homogeneous chain, reported earlier in the literature. An improvement over the homogeneous result can be obtained by representing the junctions by SQUIDs with different loop areas, so the inductances can be varied by applying a magnetic field. Still, we find that this improvement becomes less important for longer chains.
We report on experiments with superconducting Josephson metamaterials. In such a material, conventional split ring resonators are replaced by superconducting loops that are interrupted by Josephson junctions, so called rf-SQUIDs. Like the split ring resonators, they can be seen as LCresonators that couple to the magnetic component of the incoming wave. 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 show the tunability of the resonance frequency of these devices.
We propose a scheme to implement a tunable, wide frequency-band dissipative environment using a double chain of Josephson junctions. The two parallel chains consist of identical superconducting quantum interference devices (SQUIDs), with magnetic-flux tunable inductance, coupled to each other at each node via a capacitance much larger than the junction capacitance. Thanks to this capacitive coupling, the system sustains electromagnetic modes with a wide frequency dispersion. The internal quality factor of the modes is maintained as high as possible, and the damping is introduced by a uniform coupling of the modes to a transmission line, itself connected to an amplification and readout circuit. For sufficiently long chains, containing several thousands of junctions, the resulting admittance is a smooth function versus frequency in the microwave domain, and its effective dissipation can be continuously monitored by recording the emitted radiation in the transmission line. We show that by varying in situ the SQUIDs' inductance, the double chain can operate as a tunable ohmic resistor in a frequency band spanning up to 1 GHz, with a resistance that can be swept through values comparable to the resistance quantum ${R}_{q}=h/(4{e}^{2})\ensuremath{\simeq}6.5\phantom{\rule{4pt}{0ex}}\text{k}\mathrm{\ensuremath{\Omega}}$. We argue that the circuit complexity is within reach using current Josephson junction technology.
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.
We present a detailed experimental and theoretical analysis of the dispersion and nonlinear Kerr frequency shifts of plasma modes in a one-dimensional Josephson junction chain containing 500 superconducting quantum interfence devices in the regime of weak nonlinearity. The measured low-power dispersion curve agrees perfectly with the theoretical model if we take into account the Kerr renormalization of the bare frequencies and the long-range nature of the island charge screening by a remote ground plane. We measured the self- and cross-Kerr shifts for the frequencies of the eight lowest modes in the chain. We compare the measured Kerr coefficients with theory and find good agreement.
This paper investigates the physical nature of a series of step structures or oscillations present in a Josephson current within one magnetic flux quantum when either a Josephson junction, a double junction squId, or a single junction superconducting ring is placed inside a high Q cavity under the condition in which the Josephson frequency is equal to the resonance frequency of the cavity. The frequency effect of the feedback field produces a series of induced current steps in the Josephson junction or the two-junction squId when ..omega.. = ..omega../sub r/. The oscillating electromagnetic field excited by the junction current acts on the junction itself. A series of new current step structures occur within one magnetic flux phi/sub 0/ quantum, since the amplitude of the feedback field is modulated by an applied magnetic field as the modulation of the amplitude of the feedback field is coupled to that of the radiation. For the superconducting ring containing a single junction, as n..omega.. = ..omega../sub r/, the feedback radiation of the stationary electromagnetic wave will give rise to a constrained oscillation of the supercurrent with a period smaller than that of the superconducting current oscillation phi/sub 0/.