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IEEE Transactions on Applied Superconductivity

High-Linearity Bi-SQUID: Design Map

Victor K. Kornev, Nikolay V. Kolotinskiy, Daniil E. Bazulin, Oleg A. Mukhanov

Published Apr 17, 2018• 14 citations
Publisher

Abstract

We consider conditions allowing attending the highly linear voltage response of a bi-SQUID, taking into consideration the inductances of both loops and their shared inductance. The existence of the small latter one allows improving the law of the flux to phase transformation and essential enlarging margins of the high-linearity response. The reported data represent the design map for creation practical high-performance bi-SQUID-devices, taking into account a restricted fidelity in both design and fabrication.

DOI
10.1109/tasc.2018.2827982

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We consider conditions allowing attending the highly linear voltage response of a bi-SQUID, taking into consideration the inductances of both loops and their shared inductance. The existence of the small latter one allows improving the law of the flux to phase transformation and essential enlarging margins of the high-linearity response. The reported data represent the design map for creation practical high-performance bi-SQUID-devices, taking into account a restricted fidelity in both design and fabrication.
We consider and discuss a design map for bi-SQUIDs as devices capable of providing highly linear voltage response to the applied magnetic flux. The response linearity can amount to 90 to 100 dB at the optimally set parameters, the most critically, at the optimally chosen critical current of the third Josephson junction. In this paper, we summarize all our research results into a comprehensive guide for bi-SQUID design, taking into consideration all the device inductances, as well as spread in critical currents and noise impact.
We performed an in-depth numerical analysis of high-inductance bi-SQUIDs with normalized inductance of its one junction loop l ≫ 1. This is desired for better coupling with the external signals and for the high-temperature superconductor implementations. Typically the high linearity (up to 90 dB) can be achieved in bi-SQUIDs at l ≫ 1 at which its flux-to-voltage characteristic has a distinct triangular shape. We showed that the high linearity can be also achieved at l > 1, when the bi-SQUID has a hysteretic response. The critical current of the third Josephson junction is to be of the same order as the one of the other two Josephson junctions, and the inductance lDC of the second (two junction) loop is allowed to be as high as about one-fourth in the presence of the high linearity.
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.
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.
We show that the voltage response of a dc SQUID can be substantially linearized by the introduction of a nonlinear inductance. The inductance tuning allows us to achieve response linearity close to 120 dB. Such a nonlinear inductance can be easily formed using Josephson junction inductance. The additional junction and main inductance form a single-junction SQUID and hence the device can be called a bi-SQUID. To obtain high dynamic range commensurate to the high response linearity, one can use a serial array of nonlinear inductance dc SQUIDs. Experimental studies of a single bi-SQUID and serial arrays of bi-SQUIDs are reported and discussed.
We present an improved analytic theory, numerical simulation, and analysis of noise characteristics of a bi-SQUID in comparison with those of a dc SQUID in an open loop configuration. The analytic theory which had been developed earlier, neglecting a pulse component of the difference of the phases of Josephson junctions, is now completed taking into account the pulse component. In the bi-SQUID, the additional Josephson junction introduces another source of fluctuations and changes its transfer function, nonlinear dynamics, and the noise spectrum transformation. Some increase in the reduced-to-input noise at low values of applied magnetic flux comes from the nonlinear flux to phase difference transformation that was introduced in bi-SQUID as a way to linearize its voltage response.