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Physics of the Solid State

Superconducting Josephson structures with high linearity of transformation of magnetic signal into voltage

Igor I. Soloviev, Victor K. Kornev, N. V. Klenov, Oleg A. Mukhanov

Published Nov 1, 2010• 14 citations
Publisher

Abstract

Possible approaches to the creation of Josephson superconducting circuits with a high linearity of transformation of a magnetic signal into voltage and a wide dynamic range have been described. Realization of such circuit by the creation of a special spatial inhomogeneity in chains of Josephson junctions and connection of these chains into a differential circuit has been considered. A new method for linearizing the transfer function of a single two-junction superconducting quantum interference device, which is an elementary cell of the chain, by connecting to it an additional loop playing the role of a nonlinear transformer of the magnetic flux has been described. For both approaches, the basic analytical expressions describing the synthesized circuits are presented. The data on numerical calculation and experimental measurements of samples produced on the basis of niobium technology with the critical current density of Josephson junctions of 4.5 kA/cm 2 are reported. The approaches developed in the work can serve as a basis for the creation of highly efficient gigahertz superconducting amplifiers for cellular and satellite communications and can be applied for improving the characteristics of SQUID-based devices.

DOI
10.1134/s1063783410110065

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Possible approaches to the creation of Josephson superconducting circuits with a high linearity of transformation of a magnetic signal into voltage and a wide dynamic range have been described. Realization of such circuit by the creation of a special spatial inhomogeneity in chains of Josephson junctions and connection of these chains into a differential circuit has been considered. A new method for linearizing the transfer function of a single two-junction superconducting quantum interference device, which is an elementary cell of the chain, by connecting to it an additional loop playing the role of a nonlinear transformer of the magnetic flux has been described. For both approaches, the basic analytical expressions describing the synthesized circuits are presented. The data on numerical calculation and experimental measurements of samples produced on the basis of niobium technology with the critical current density of Josephson junctions of 4.5 kA/cm 2 are reported. The approaches developed in the work can serve as a basis for the creation of highly efficient gigahertz superconducting amplifiers for cellular and satellite communications and can be applied for improving the characteristics of SQUID-based devices.
Abstract A superconducting quantum interference device with differential output or ‘DSQUID’ was previously proposed for operation in the presence of large common-mode signals. The DSQUID is the differential connection of two identical SQUIDs. Here we show that besides suppression of electromagnetic interference this device provides effective linearization of the DC SQUID voltage response. In the frame of the resistive shunted junction model with zero capacitance, we demonstrate that spur-free dynamic range of the DSQUID magnetic flux-to-voltage transfer function is higher than 100 dB while the total harmonic distortion of a signal is less than 10 −3 % with a peak-to-peak amplitude of a signal being a quarter of half flux quantum, 2Φ a = Φ 0 /8. Analysis of the DSQUID voltage response stability to a variation of circuit parameters shows that DSQUID implementation allows for highly linear magnetic flux-to-voltage transformation at the cost of a high identity of Josephson junctions and high-precision current supply.
We develop a two-dimensional (2-D) superconducting quantum interference filter (SQIF) array based on the recently introduced high-linearity tri-junction bi-SQUIDs (superconducting quantum interference device). Our bi-SQUID SQIF array design is based on a tight integration of individual bi-SQUID cells sharing inductances with adjacent cells. We provide extensive computer simulations, analysis, and experimental measurements, in which we explore the phase dynamics and linearity of the array voltage response. The nonuniformity in inductances of the bi-SQUIDs produces a pronounced zero-field single antipeak in the voltage response. The antipeak linearity and size can be optimized by varying the critical current of the additional junction of each bi-SQUID. The layout implementation of the tight 2-D array integration leads to a distinct geometrical diamond shape formed by the merged dual bi-SQUID cells. Different-sized 2-D arrays are fabricated using the standard HYPRES niobium 4.5 kA/cm2fabrication process. The measured linearity, power gain, and noise properties will be analyzed for different array sizes and the results will be compared with circuit simulations. We will discuss a design approach for the electrically small magnetic field antenna and low-noise amplifiers with high bandwidth based on these 2-D bi-SQUID SQIF arrays. The results from this work will be used to design chips densely and completely covered in bi-SQUIDs that have optimized parameters such as linearity and power gain.
Superconducting double-loop interferometers (bi-SQUIDs) have been introduced to produce magnetic flux sensors specifically designed to exhibit an ultrahighly linear voltage response as a function of the magnetic flux. These devices are very important for quantum sensing and for signal processing of signals oscillating in the radio-frequency range of the electromagnetic spectrum. Here, we report an Al\mathrm{Al}Al double-loop bi-SQUID based on proximitized mesoscopic Cu\mathrm{Cu}Cu Josephson junctions. Such a scheme provides an alternative fabrication approach to conventional tunnel-junction-based interferometers, where the junction characteristics and, consequently, the magnetic-flux-to-voltage and magnetic-flux-to-critical-current device responses can be largely and easily tailored by the geometry of the metallic weak links. We discuss the performance of such sensors by showing a full characterization of the device switching current and voltage drop versus the magnetic flux for operation temperatures ranging from 30 mK to approximately 1K1\phantom{\rule{0.2em}{0ex}}\mathrm{K}1K. The figures of merit of the transfer function and of the total harmonic distortion are also discussed. The latter provides an estimate of the linearity of the flux-to-voltage device response, which attains values as large as 45 dB. Such a result lets us foresee a performance already on par with that achieved in conventional tunnel-junction-based bi-SQUIDs arrays composed of hundreds of interferometers.
It is proposed the solution of an urgent problem of developing broadband superconducting devices via implementation of multi-element Josephson structures with an expanded dynamic range (due to the increase in the number of cells) and required high linearity of the transfer function of magnetic signal into voltage (due to the use of specially designed Josephson cells with a highly linear voltage response). Active electrically small antenna prototypes based on the proposed multi-element structures are experimentally studied.
The Josephson effect, tunnelling of a supercurrent through a thin insulator layer between two superconducting islands, is a phenomena characterized by a spatially distributed phase of the superconducting condensate. In recent years, there has been a growing focus on Josephson junction devices particularly for the applications of quantum metrology and superconducting qubits. In this study, we report the development of Josephson junction circuit formed by serially connecting many Superconducting Quantum Interference Devices, SQUIDs. We present experimental measurements as well as numerical simulations of a phase-slip center, a SQUID with weaker junctions, embedded in a Josephson junction chain. The DC transport properties of the chain are the result of phase slips which we simulate using a classical model that includes linear external damping, terminating impedance, as well as internal nonlinear quasiparticle damping. We find good agreement between the simulated and the experimental current voltage characteristics. The simulations allow us to examine the spatial and temporal distribution of phase-slip events occurring across the chains and also the existence of travelling voltage pulses which reflect at the chain edges.
Superconducting quantum interference devices (SQUIDs), single flux-quantum (SFQ) logic circuits, and quantum Josephson junction circuits have been developed into a family of superconductor integrated circuit, and are widely applied for subtle magnetic-field measurements, energy-efficient computing, and quantum computing, respectively. They are Josephson junction networks composed of Josephson junctions and normal resistor-inductor-capacitor (RLC) components, working with the fluxoid-quantization principle and Josephson effects to achieve unique flux-modulated dynamics and characteristics; they react to the vector potential of magnetic fields rather than the electric potential. However, the conventional circuit diagrams and nodal analysis methods focus on the electric charges flowing though branches and nodes, ignoring dynamics of the magnetic fluxes flowing from loop to loop. This article introduces a general flux-based circuit theory to unify the analyses of Josephson junction circuits and normal RLC circuits. This theory presents a magnetic-flux-generator (MFG) concept to unify Josephson junctions and normal circuit elements, and abstract both Josephson junction circuits and normal RLC circuits as MFG network; it derives a general network equation to describe dynamics of Josephson junction circuits, and invents a kind of magnetic-flux flow (MFF) diagram to depict the working principles of magnetic-flux flows inside Josephson junction circuits. The flux-based theory is complementary to the conventional circuit theories in the design and analysis of superconductor integrated circuits.