Ultrahigh Linearity of the Magnetic-Flux-to-Voltage Response of Proximity-Based Mesoscopic Bi-SQUIDs

Giorgio De Simoni, Lorenzo Cassola, Nadia Ligato, Giuseppe C. Tettamanzi, and Francesco Giazotto

Phys. Rev. Applied 18, 014073 – Published 28 July 2022

Abstract

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 $Al$ double-loop bi-SQUID based on proximitized mesoscopic $Cu$ 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 $1 K$ . 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.

Received 14 January 2022
Revised 18 March 2022
Accepted 7 June 2022
Corrected 17 August 2022

DOI:https://doi.org/10.1103/PhysRevApplied.18.014073

Physics Subject Headings (PhySH)

Josephson junctions Optoelectronics Proximity effect Quantum sensing Radio frequency techniques Solid-state detectors

Nanostructures SQUID

Condensed Matter, Materials & Applied Physics

Corrections

17 August 2022

Correction: The author order was presented incorrectly and has been fixed.

Authors & Affiliations

Giorgio De Simoni ^1,*, Lorenzo Cassola ^1,2, Nadia Ligato¹, Giuseppe C. Tettamanzi ³, and Francesco Giazotto^1,†

¹NEST, Istituto Nanoscienze – CNR and Scuola Normale Superiore, Pisa I-56127, Italy
²Department of Physics “E. Fermi,” Università di Pisa, Largo Pontecorvo 3, Pisa I-56127, Italy
³Institute of Photonics and Advanced Sensing and School of Physical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia

^*giorgio.desimoni@sns.it
^†francesco.giazotto@sns.it

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 18, Iss. 1 — July 2022

Subject Areas

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
A proximity-based all-metallic bi-SQUID. (a) A false-color scanning electron micrograph of a representative double-loop dc superconducting quantum interference device (bi-SQUID) based on superconductor–normal-metal–superconductor ( $S$ - $N$ - $S$ ) proximity Josephson junctions. The $Al$ interferometer ring is colored in blue. The $Cu$ Josephson weak links are colored in brown. The four-wire electrical setup is also shown. (b) A higher-magnification false-color scanning electron micrograph of the second loop of the bi-SQUID. The $Cu$ weak links are labeled as $A$ , $B$ , and $C$ . (c) The current ( $I$ ) versus voltage ( $V$ ) forward and backward characteristics of a representative bi-SQUID at selected temperatures between 30 mK and 900 mK and at zero magnetic flux. The curves are horizontally offset for clarity. The $I$ - $V$ nondissipative region is shaded in gray. (d) The switching (violet) and retrapping (green) current of the same device as in (a) versus the temperature $T$ .
Reuse & Permissions
Figure 2
The switching current versus the flux characterization of the $S$ - $N$ - $S$ SQUID. (a) The switching current $I_{S}$ of the bi-SQUID as a function of the out-of-plane magnetic field $B$ for selected bath temperatures ranging from 30 mK to 700 mK. The external out-of-plane magnetic field is applied through a superconducting electromagnet. $I_{S} (B)$ is shown for selected temperatures ranging between 30 mK and 700 mK. (b) The critical-current modulation visibility $v = 2 (I_{S_{ma x}} - I_{S_{mi n}}) / (I_{S ma x} + I_{S_{mi n})}$ versus the temperature $T$ . (c) A plot of the numerical $I_{S} (ϕ)$ obtained through a resistively shunted junction (RSJ) fit of the experimental data of Fig. 2. (d) The asymmetry parameters $α$ (blue dots) and $α_{3}$ (green dots) as a function of the temperature. The error bars represent the $95 %$ confidence bound for the parameter value returned by the fit procedure. (e) The screening parameters $β_{1}$ (blue dots) and $β_{2}$ (green dots) as a function of the temperature. The values reported in (d) and (e) are extracted through the fitting procedure (see text). The error bars represent the $95 %$ confidence bound for the parameter value returned by the fit procedure.
Reuse & Permissions
Figure 3
A $S$ - $N$ - $S$ bi-SQUID operated in the dissipative regime. (a) The voltage-flux response curves numerically calculated through an RSJ model ( $V (ϕ_{1}) = R_{N} \sqrt{I^{2} - I_{S}^{2}}$ ) at selected relative current bias $I / I_{S}$ . The curves are calculated by means of the numerical $I_{S} (ϕ_{1})$ derived from the fit of the experimental data of Fig. 2 at 30 mK. (b) The four-wire lock-in $V (ϕ_{1})$ characteristics at 30 mK for selected values of the root-mean-square (rms) bias current $I$ between $3 μ A$ and $6.4 μ A$ , measured by biasing the device with a 17-Hz sinusoidal current signal. Below $I ≃ 21.5 μ A$ , the curves show null voltage drop when $I < I_{S} (ϕ_{1})$ . A finite $V$ value is measured when the device is in the dissipative regime, i.e., when $I$ is larger than the flux-dependent switching current. (c) The four-wire lock-in $V (ϕ)$ characteristics at selected temperature between 30 mK and 500 mK. $I$ is chosen at each temperature in order to let the device operate permanently in the dissipative regime and to maximize the linearity of the voltage-flux response (see text). $I$ is set to $21.5 μ A$ , $21 μ A$ , $20 μ A$ , $16 μ A$ , $13 μ A$ , and $9 μ A$ for $T$ equal to 30 mK, 100 mK, 200 mK, 300 mK, 400 mK, and 500 mK, respectively. (d) The maximum value $f_{t_{M}}$ of the transfer function ( $f_{t}$ ) versus $I_{rm s}$ . The empty circles correspond to $f_{t}$ values obtained in the mixed superconductive-dissipative regime and the filled circles to the fully resistive regime. The dashed vertical gray line separates the two regimes. (e) The maximum value $f_{t_{M}}$ of the transfer function ( $f_{t}$ ) versus $T$ . The plotted values are obtained in the fully resistive regime.
Reuse & Permissions
Figure 4
The linearity of the voltage-flux response of the $S$ - $N$ - $S$ bi-SQUIDs extracted from the experimental data. (a) The total harmonic distortion $L = - 20 lo g (\sqrt{\sum_{n = 2}^{\infty} A_{n}^{2}} / A_{1})$ versus $I$ for selected values of the flux-modulation amplitude $Φ$ , between $ϕ_{0} / 8$ and $ϕ_{0} / 16$ . The dashed lines are guides for the eye. (b) The temperature- $T$ evolution of the linearity $L$ . The inset shows a schematic of the method exploited to extract $L$ from the $V (ϕ_{1})$ characteristics. A sinusoidal modulation $Φ si n (ω_{1})$ of the flux around the working point $\bar{ϕ}$ with arbitrary frequency $ω_{1} / 2 π$ translates into a voltage signal through the experimental flux-to-voltage response curves [plotted in Figs. 3 and 3]. The resulting signal is then fast Fourier transformed to compute $L$ .
Reuse & Permissions

Physical Review Applied