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Europhysics Letters (EPL)

Frequency spectrum of a superconducting metadevice

James A. Blackburn, Matteo Cirillo, Niels Grønbech‐Jensen

Published Oct 13, 2016• 6 citations
Publisher

Abstract

We report on a systematic analysis of the frequency spectrum of a system often considered for quantum computing purposes, metadevice applications, and high-sensitivity sensors, namely a superconducting loop interrupted by Josephson junctions, the core of an rf-SQUID.We analyze both the cases in which a single junction closes the superconducting loop and the one in which the single junction is replaced by a superconducting interferometer.Perturbation analysis is employed to display the variety of the solutions of the system and the implications of the results for the present interest in fundamental and applied research are analyzed.

DOI
10.1209/0295-5075/115/50004

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We report on a systematic analysis of the frequency spectrum of a system often considered for quantum computing purposes, metadevice applications, and high-sensitivity sensors, namely a superconducting loop interrupted by Josephson junctions, the core of an rf-SQUID.We analyze both the cases in which a single junction closes the superconducting loop and the one in which the single junction is replaced by a superconducting interferometer.Perturbation analysis is employed to display the variety of the solutions of the system and the implications of the results for the present interest in fundamental and applied research are analyzed.
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.
At low temperature and low damping, the magnetic flux of a rf Superconducting QUantum Interference Device (SQUID) acts as a macroscopic quantum variable whose dynamic is described by a double well potential. A rf SQUID consists of a superconducting loop interrupted by a thin insulating barrier, known as a Josephson junction. The modified rf SQUID design discussed in this thesis has independent, in situ, controls that allow varying the barrier height between the potential wells and their relative tilt. This high level of control of the potential together with the capability to implement an experimental setup optimized to reduce coupling to external sources of noise, made this system ideal not only for tests of quantum transition at a macroscopic level, but also as a scalable solid state device for quantum computation. A variety of measurements of quantum phenomena are reported in this thesis, including microwave level spectroscopy, coherent oscillations, and macroscopic resonant tunneling (MRT). These measurements are compared with theoretical models to study the possible sources of decoherence in a rf SQUID qubit. The analysis confirmed that the main source of decoherence is not due to coupling to the external environment, but it can be linked to intrinsic low frequency flux noise. Work from many groups over the last several years has shown that the performance of a superconductive qubit is limited by coupling to spurious defects in the materials used for the device fabrication. In this work we analyze the possibility of using the MRT as a tool for future studies of effects of materials and fabrication process in the realization of improved qubits, and we also explore the feasibility for measurements of quantum phenomena that involve fast pulsing of the potential barrier height.
In Chapter 2 we made use of a hypothetical arrangement of a strongly coupled superconducting ring, interrupted by a region of weak superconductivity, to derive the essential features of the Josephson effects. In practice this same arrangement is actually employed as the basis of one of the most useful superconducting devices developed so far, the single-junction, or rf, squid . (As mentioned in the Introduction, squid is an acronym for Superconducting QUantum Interference Device.) Here the essential physics behind the operation of these important devices will be described, and in the following section the practical realisation of an rf squid with its associated readout electronics will be explained. Chapter 4 will treat in a similar way dc squid s, which are related devices possessing two weak links in a single ring, whose mode of operation is rather different.
Abstract Superconducting quantum interference devices (SQUIDs) are made by a superconducting loop interrupted by one or more Josephson junctions. They are described in terms of a macroscopic variable, the magnetic flux, which shows quantum effects such as tunnelling through a potential barrier. Besides making up the source of a quantum state, SQUIDs also provide the instruments necessary for its probing: as a fact, SQUID based magnetometers have a sensitivity approaching the quantum limit. In this paper I will review the working principle of these devices and illustrate the system of SQUIDs realized in my group to test the quantum behavior at a macroscopic level.
Abstract We consider, for the first time, the effects of strong capacitive and inductive coupling between radio frequency superconducting quantum interference devices (rf SQUIDs) in an overlapping metamaterial geometry when driven by rf flux at and near their self-resonant frequencies. The equations of motion for the gauge-invariant phases on the Josephson junctions in each SQUID are set up and solved. Our model accounts for the high-frequency displacement currents through capacitive overlap between the wiring of SQUID loops. We begin by modeling two overlapping SQUIDs and studying the response in both the linear and nonlinear high-frequency driving limits. By exploring a sequence of more and more complicated arrays, the formalism is eventually extended to the N × N × 2 overlapping metamaterial array, where we develop an understanding of the many ( 8 N 2 − 8 N + 3 ) resulting resonant modes in terms of three classes of resonances. The capacitive coupling gives rise to qualitatively new self-resonant responses of rf SQUID metamaterials, and is demonstrated through analytical theory, numerical modeling, and experiment in the 10–30 GHz range on capacitively and inductively coupled rf SQUID metamaterials.
The superconducting quantum interferometer with two quantization loops, the so-called double SQUID, or D-SQUID, is a modification of the well-known rf SQUID. The modification consists of a replacement of the one junction of the rf SQUID by a superconducting loop with two Josephson junctions. This device can be used to transform the weak magnetic flux applied to the loop with junctions to a voltage across the tank circuit inductively coupled to the other loop. As has previously been shown in experiments [G. S. Krivoy and H. Koch, J. Appl. Phys. 74, 2925 (1993)], D-SQUIDs have an extremely large output signal swing up to 1 mV and a transfer function of several mV/(h/2e). In this paper, a D-SQUID theory using a numerical and an analytical approach is developed. The theoretical results are compared with the above-mentioned experiments.