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arXiv:2511.15020 · Physical Review Applied

Synthetic area spread in two-dimensional arrays of superconducting quantum interference filters

Ross D. Monaghan, J. L. Marenkovic, Giuseppe Carlo Tettamanzi

Published Oct 2, 2026• 0 citations
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Abstract

Superconducting Quantum Interference Devices (SQUIDs), formed by incorporating Josephson junctions into loops of superconducting material, are the backbone of many modern quantum sensing systems. It has been demonstrated that, by combining multiple SQUID loops into a two-dimensional (2D) array, it is possible to fabricate ultra-high-performing radio-frequency sensors. However, to function as absolute magnetometers, current-in-use arrays require the area of each SQUID loop in the array to be incommensurate. Doing so forbids the achievement of their full potential of performance, limited only by the standard quantum limit. This is because imposing incommensurability in the areas contrasts with optimised performance in each single SQUID loop. In this work, we report that by selectively inserting bare sections of a superconducting circuit with no Josephson junctions, 2D SQUID arrays can operate as an absolute magnetometer even when no physical area spread is applied. Based on a generalisation of currently available theories, a complete analytical formulation for the one-to-one correspondence between the distribution of these bare loops and what we call a synthetic areas spread is unveiled. This synthetic spread represents the equivalent physical spread of incommensurate SQUID loops that you would use to obtain the absolute Voltage-Magnetic Flux response if no bare loops were in use. Our work opens the way to a broader use of this technology for the fabrication of ultra-high-performance absolute quantum sensors. Our approach is also experimentally verified by fabricating several 2D Superconducting Quantum Interference Filter (SQIF) arrays incorporating bare superconducting loops and by demonstrating that they behave in alignment with what is suggested by our theory.

DOI
10.1103/wc1k-wxtc

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Superconducting Quantum Interference Devices (SQUIDs), formed by incorporating Josephson junctions into loops of superconducting material, are the backbone of many modern quantum sensing systems. It has been demonstrated that, by combining multiple SQUID loops into a two-dimensional (2D) array, it is possible to fabricate ultra-high-performing radio-frequency sensors. However, to function as absolute magnetometers, current-in-use arrays require the area of each SQUID loop in the array to be incommensurate. Doing so forbids the achievement of their full potential of performance, limited only by the standard quantum limit. This is because imposing incommensurability in the areas contrasts with optimised performance in each single SQUID loop. In this work, we report that by selectively inserting bare sections of a superconducting circuit with no Josephson junctions, 2D SQUID arrays can operate as an absolute magnetometer even when no physical area spread is applied. Based on a generalisation of currently available theories, a complete analytical formulation for the one-to-one correspondence between the distribution of these bare loops and what we call a synthetic areas spread is unveiled. This synthetic spread represents the equivalent physical spread of incommensurate SQUID loops that you would use to obtain the absolute Voltage-Magnetic Flux response if no bare loops were in use. Our work opens the way to a broader use of this technology for the fabrication of ultra-high-performance absolute quantum sensors. Our approach is also experimentally verified by fabricating several 2D Superconducting Quantum Interference Filter (SQIF) arrays incorporating bare superconducting loops and by demonstrating that they behave in alignment with what is suggested by our theory.
The superconducting quantum interference filter (SQIF) is a new type of superconducting device which has been recently proposed for highly sensitive magnetometers for absolute magnetic field measurements. It benefits of very high voltage-to-field response, which is, in contrast conventional dc SQUIDs, not periodical. The SQIF can also be used as a radiofrequency amplifier in a similar way as the dc SQUID that can operate in a gigahertz frequency range. We designed a series type of SQIF amplifier that is compatible to conventional YBa2Cu3O7(YBCO) technology on bicrystal substrates. We present analytical, numerical and scale modeling as well as first electrical measurements results at frequencies up to 10 GHz. The SQIF array consists of 50 loops with randomly distributed areas from 0.5 to 1.5 times of . We also compared it to the regular array of conventional SQUIDs with the same loop areas. We have additional dc contacts to each 5-th SQUIDs and the SQIFs for control and comparison. Devices are fabricated using Josephson junctions with 3 mum width formed in YBCO over 24/24 and 12/12 degrees grain boundaries in yttrium-stabilized zirconia (YSZ) bicrystal substrates.
We have successfully developed a novel superconducting quantum interferometer based on Josephson junction networks with unconventional loop size distribution. For distinct theoretically determined distributions, the magnetic field B dependent dc voltage V(B) of the interferometer possesses a unique delta-peak like characteristics around B=0. Such devices are called Superconducting Quantum Interference Filters (SQIFs). The unique voltage response of SQIFs allows novel applications, e.g., absolute magnetic field sensors, high speed logical switches and non hysteretic low noise amplifiers which can be directly connected to standard room temperature electronics. In this paper we present new experimental and theoretical results on high performance two dimensional Superconducting Quantum Interference Filters (2D SQIFs). Such 2D SQIFs can be used as absolute magnetic field sensors. Our results indicate that due to the scaling behavior of the flux to voltage transfer function and the scaling of the white output noise, a highly sensitive absolute field sensor based on 2D SQIFs can be very small in size.
We present experimental results on the magnetic field B dependent voltage response V(B) of a number of N resistively shunted Josephson junctions connected in parallel by a multiple loop network. For an appropriate distribution of the array loop sizes, such networks constitute superconducting quantum interference filters (SQIFs) with voltage response functions V(B) that are not /spl Phi//sub 0/-periodic. The voltage response of SQIFs is a unique function around a global minimum at B=0 that has a high sensitivity and a low noise level. In contrast to conventional superconducting quantum interference devices, SQIFs can be directly employed as highly sensitive magnetometers allowing the absolute measurement of magnetic fields. The experimental results are in very good agreement with the theoretical predictions on which basis the SQIF has been fabricated, All findings suggest that superconducting quantum interference filters may allow the design of novel superconducting devices.
Series arrays of superconducting quantum interference devices (SQUIDs) with incommensurate loop areas, so-called superconducting quantum interference filters (SQIFs), are investigated in the kilohertz and the gigahertz frequency range. In SQIFs made of high-Tc bicrystal junctions the flux-to-voltage response ∂V/∂Φ is dominated by the variation in the critical current in the individual junctions (Fraunhofer-type) rather than by the SQUIDs interference. For a SQIF with 20 SQUID loops we find ∂V/∂Φ=40 mV/Φ0 and a dynamic range of more than 60 dB in the kilohertz range. In the 1–2 GHz range the estimated power gain is 20 dB and the magnetic flux noise level is as low as 10−4Φ0.
We present a theoretical model for two-dimensional (2D) superconducting quantum interference device (SQUID) and superconducting quantum interference filter (SQIF) arrays with overdamped Josephson junctions for uniform bias-current injection at 77 K. Our simulations demonstrate the importance of including Johnson thermal noise and reveal that only the SQUID-loops self-inductance contributions are of importance. Our numerical results establish the validity of a scaling behavior between the voltages of one-dimensional (1D) and 2D SQUID arrays and show that the same scaling behavior applies to the maximum transfer functions. The maximum transfer function of a 2D SQUID array can be further optimized by applying the optimal bias current, which depends on the SQUID-loop self-inductance and the junction critical current. Our investigation further reveals that a scaling behavior exists between the maximum transfer function of a 2D SQUID array and that of a single dc SQUID. Finally, we investigate the voltage response of 1D and 2D SQIF arrays and illustrate the effects of adding spreads in the heights and widths of SQUID loops.
We have fabricated arrays of High-Tc Superconducting Quantum Interference Devices (SQUIDs) with randomly distributed loop sizes as sensitive detectors for Radio Frequency (RF) waves. These subwavelength size devices known as Superconducting Quantum Interference Filters (SQIFs) detect the magnetic component of the electromagnetic field. We used a scalable ion irradiation technique to pattern the circuits and engineer the Josephson junctions needed to make SQUIDs. Here, we report on a 300 SQUID series array with the loop area ranging from 6 to 60 μm2, folded in a meander line covering a 3.5 mm × 120 μm substrate area, made out of a 150 nm thick YBa2Cu3O7 film. Operating at a temperature of T = 66 K in an unshielded magnetic environment under low DC bias current (I = 60 μA) and a DC magnetic field (B = 3 μT), this SQIF can detect a magnetic field of a few picoteslas at a frequency of 1.125 GHz, which corresponds to a sensitivity of a few hundreds of fT/Hz and shows a linear response over 7 decades in RF power. This work is a promising approach for the realization of low dissipative subwavelength gigahertz magnetometers.