^{1,a)}, Susan Berggren

^{2}, Anna Leese de Escobar

^{1}, Antonio Palacios

^{2}, Sarah Rice

^{1}, Benjamin Taylor

^{1}, Visarath In

^{1}, Oleg A. Mukhanov

^{3}, Georgy Prokopenko

^{3}, Martin Nisenoff

^{4}, Edmond Wong

^{1}and Marcio C. De Andrade

^{1}

### Abstract

Multi-loop arrays of Josephson junctions (JJs) with non-uniform area distributions, which are known as superconducting quantum interference filters (SQIFs), are the most highly sensitive sensors of changes in applied magnetic field as well as the absolute magnitude of magnetic fields. The non-uniformity of the loop sizes allows the array to produce a unique collective voltage response that has a pronounced single peak with a large voltage swing around zero magnetic field. To obtain high linear dynamic range, which is critical for a wide variety of applications, the linearity of the slope of the anti-peak response must be improved. We propose a novel scheme for enhancing linearity—a new configuration combining the SQIF array concept with the recently introduced bi-superconductive quantum interference device (SQUID) configuration, in which each individual SQUID loop is made up of three JJs as opposed to using two JJs per loop in standard dc SQUIDs. We show, computationally, that the additional junction offers a viable linearization method for optimizing the voltage response and dynamic range of SQIF arrays. We have realized SQIF arrays based on bi-SQUID cells and present first experimental results.

We gratefully acknowledge support from the Tactical SIGINT Technology Program N66001-08-D-0154. We also wish to acknowledge support from the Office of Naval Research (ONR), Code 30, ONR NREIP Internship Program, the SPAWAR internal research funding (S&T) program, SPAWAR SBIR contracts N00039-08-C-0024 and N66001-09-R-0073. O. M. and G. P. thank V. Kornev, I. Soloviev, N. Klenov, A. Sharafiev for useful discussion related to bi-SQUID designs, D. Kirichenko for useful design and test advices, S. Tolpygo, R. Hunt, J. Vivalda, D. Yohannes, D. Amparo for chips fabrication, and V. Dotsenko for cryoprobe design and fabrication.

I. INTRODUCTION

II. BACKGROUND

A. The dc SQUID

B. The dc bi-SQUID

III. SERIAL BI-SQUID ARRAY

IV. PARALLEL BI-SQUID ARRAY

V. CIRCUIT DESIGN, FABRICATION, AND EXPERIMENTAL EVALUATION

A. Physical circuit simulation

B. Design and fabrication

VI. CONCLUSION

### Key Topics

- Josephson junctions
- 27.0
- Critical currents
- 24.0
- Superconducting quantum interference devices
- 20.0
- Magnetic flux
- 9.0
- Magnetic fields
- 8.0

## Figures

(Top) Schematic diagram of a dc SQUID magnetometer together with (bottom) the time-averaged voltage response between the two junctions, as a function of the normalized external magnetic flux .

(Top) Schematic diagram of a dc SQUID magnetometer together with (bottom) the time-averaged voltage response between the two junctions, as a function of the normalized external magnetic flux .

(Top) Schematic diagram of a dc bi-SQUID magnetometer together with (bottom) its time-averaged voltage response between the two junctions, as a function of the normalized external magnetic flux .

(Top) Schematic diagram of a dc bi-SQUID magnetometer together with (bottom) its time-averaged voltage response between the two junctions, as a function of the normalized external magnetic flux .

Circuit representation of a dc bi-SQUID device. “P” is a phase source that accounts for the phase shift due to the external magnetic flux .

Circuit representation of a dc bi-SQUID device. “P” is a phase source that accounts for the phase shift due to the external magnetic flux .

(Top) Numerical simulations of the voltage response of a single bi-SQUID as a function of the critical current . Parameters are , , , , and . (Bottom) Linearity test via linear fitting error and through calculations of SFDR. Observe that best linear response is directly correlated with highest SFDR. Development of cusp for .

(Top) Numerical simulations of the voltage response of a single bi-SQUID as a function of the critical current . Parameters are , , , , and . (Bottom) Linearity test via linear fitting error and through calculations of SFDR. Observe that best linear response is directly correlated with highest SFDR. Development of cusp for .

Circuit representation of an array of bi-SQUID devices connected in series. “P” is a phase source that accounts for the phase shift due to the external magnetic flux .

Circuit representation of an array of bi-SQUID devices connected in series. “P” is a phase source that accounts for the phase shift due to the external magnetic flux .

Numerical simulations of the voltage response of a non-uniform serial bi-SQUID array ( ) as a function of the critical current and external flux . Loop sizes are selected according to a Gaussian distribution. , , , and .

Numerical simulations of the voltage response of a non-uniform serial bi-SQUID array ( ) as a function of the critical current and external flux . Loop sizes are selected according to a Gaussian distribution. , , , and .

Linearity test (dashed line) via linear fitting error of the voltage response of an array of equals bi-SQUID devices connected in series as a function of the critical current and corresponding SFDR (solid line). The test shows that there exists a critical current where the error decreases significantly such that the linearity increases. It also shows an optimal value of the critical current where SFDR is optimum and beyond which only marginal improvements in linearity can be achieved.

Linearity test (dashed line) via linear fitting error of the voltage response of an array of equals bi-SQUID devices connected in series as a function of the critical current and corresponding SFDR (solid line). The test shows that there exists a critical current where the error decreases significantly such that the linearity increases. It also shows an optimal value of the critical current where SFDR is optimum and beyond which only marginal improvements in linearity can be achieved.

Circuit representation of an array of bi-SQUID devices connected in parallel. “P” is a phase source that accounts for the phase shift due to the external magnetic flux .

Circuit representation of an array of bi-SQUID devices connected in parallel. “P” is a phase source that accounts for the phase shift due to the external magnetic flux .

Numerical simulations of the voltage response of a non-uniform parallel bi-SQUID array as a function of the critical current and external flux . Loop sizes are selected according to a Gaussian distribution. Other parameters are the same as in Fig. 6 .

Numerical simulations of the voltage response of a non-uniform parallel bi-SQUID array as a function of the critical current and external flux . Loop sizes are selected according to a Gaussian distribution. Other parameters are the same as in Fig. 6 .

Comparison of the average voltage response as a function of magnetic flux for: a single bi-SQUID (dashed) and two arrays of bi-SQUIDs, one connected in series (black) and one connected in parallel (gray).

Comparison of the average voltage response as a function of magnetic flux for: a single bi-SQUID (dashed) and two arrays of bi-SQUIDs, one connected in series (black) and one connected in parallel (gray).

(a) Schematic of a single bi-SQUID cell, rendered in MWO for time domain simulations, including measurement setup for averaging Josephson oscillations. The schematic parameters are chosen as critical current of all three junction are the same, , first two junctions are resistively shunted with , , the third junction is unshunted. . (b) Simulated voltage-flux (control) current response of a single bi-SQUID.

(a) Schematic of a single bi-SQUID cell, rendered in MWO for time domain simulations, including measurement setup for averaging Josephson oscillations. The schematic parameters are chosen as critical current of all three junction are the same, , first two junctions are resistively shunted with , , the third junction is unshunted. . (b) Simulated voltage-flux (control) current response of a single bi-SQUID.

Simulated voltage-flux (control) current response of 10-cell bi-SQUID SQIF arrays with normal distribution of inductances and junction critical current . Only two junctions are shunted with , , the third junction left unshunted. (a) Serial 10 bi-SQUID SQIF array. (b) Parallel 10 bi-SQUID SQIF array.

Simulated voltage-flux (control) current response of 10-cell bi-SQUID SQIF arrays with normal distribution of inductances and junction critical current . Only two junctions are shunted with , , the third junction left unshunted. (a) Serial 10 bi-SQUID SQIF array. (b) Parallel 10 bi-SQUID SQIF array.

Physical structures of bi-SQUID SQIF arrays implemented using HYPRES superconductor fabrication process: (a) microphotograph of the fabricated serial array fragment, (b) microphotograph of the fabricated parallel array fragment, and (c) the MWO-generated 3D sketch of a bi-SQUID cell from the serial array.

Physical structures of bi-SQUID SQIF arrays implemented using HYPRES superconductor fabrication process: (a) microphotograph of the fabricated serial array fragment, (b) microphotograph of the fabricated parallel array fragment, and (c) the MWO-generated 3D sketch of a bi-SQUID cell from the serial array.

Microphotographs of the fabricated bi-SQUID-SQIFs integrated on 5 mm × 5 mm chips. (a) Serial meander arrays consisting of 256 bi-SQUID cells. (b) A set of parallel 10 bi-SQUID cell arrays. (c) Serial meander SQIF array with 1445 bi-SQUID cells. (d) Serial spiral SQIF array with 1315 biSQUID cells.

Microphotographs of the fabricated bi-SQUID-SQIFs integrated on 5 mm × 5 mm chips. (a) Serial meander arrays consisting of 256 bi-SQUID cells. (b) A set of parallel 10 bi-SQUID cell arrays. (c) Serial meander SQIF array with 1445 bi-SQUID cells. (d) Serial spiral SQIF array with 1315 biSQUID cells.

Measured flux-voltage characteristics of bi-SQUID SQIF arrays: (a) a serial 256 bi-SQUID array. Voltage-flux (V-F) response with , , maximum voltage , coefficient of transformation is for ( is flux quantum); (b) a parallel 10 bi-SQUID array with , , maximum voltage , coefficient of transformation is for ; (c) serial meander 1445-cell array with , ; maximum voltage , coefficient of transformation for ; and (d) serial spiral 1315-cell array with , ; maximum voltage , coefficient of transformation for .

Measured flux-voltage characteristics of bi-SQUID SQIF arrays: (a) a serial 256 bi-SQUID array. Voltage-flux (V-F) response with , , maximum voltage , coefficient of transformation is for ( is flux quantum); (b) a parallel 10 bi-SQUID array with , , maximum voltage , coefficient of transformation is for ; (c) serial meander 1445-cell array with , ; maximum voltage , coefficient of transformation for ; and (d) serial spiral 1315-cell array with , ; maximum voltage , coefficient of transformation for .

Spur free dynamic range of an array of dc bi-SQUID loops connected in series.

Spur free dynamic range of an array of dc bi-SQUID loops connected in series.

Circuit representation of the nearest neighbors of the bi-SQUID in a parallel array. “P” is the normalized applied magnetic flux .

Circuit representation of the nearest neighbors of the bi-SQUID in a parallel array. “P” is the normalized applied magnetic flux .

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