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Journal of Physics Condensed Matter

Capacitance in a radio-frequency-SQUID magnetometer

Jason F. Ralph, Terrence D. Clark, Robert J. Prance, Helen Prance, J. Diggins

Published Dec 2, 1996• 11 citations
Publisher

Abstract

We use a discrete-field model for the quantum evolution of distributed superconducting circuits to calculate the effective capacitance for a radio-frequency-SQUID magnetometer: a large-capacitance superconducting ring containing an ultra-small-capacitance weak link. We demonstrate that the self-capacitance of the weak link can dominate the behaviour of the circuit.

DOI
10.1088/0953-8984/8/49/058

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Starting with a simple Lagrangian for the electromagnetic field with broken gauge symmetry, we derive an effective circuit Hamiltonian for a superconducting weak-link ring. The energy eigenstates of this Hamiltonian exhibit sensitivity to both external magnetic flux and an applied Faraday law voltage. We show that the flux periodicity of the rf SQUID ring, and the voltage periodic behaviour found in ultra-small-capacitance weak-link rings, can be seen as limiting cases of a more general phenomenon.
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The Josephson effect, as an example of a macroscopic quantum phenomenon, reveals itself in the three-layer heterostructures formed by two superconductors coupled by a weak link that usually consists of a 1-2 nm-thick insulating barrier.The traditional way of modelling such-systems' dynamics is based on an equivalent circuit that comprises three parallel elements: a pure superconducting element with a certain supercurrent-versus-Josephson phase difference dependence, a resistor R, and a capacitor C. In this short review, we analyse the practical problem of reducing the junction capacitance while maintaining or slightly impairing other characteristics.Some arguments are presented to explain why the capacitance should be suppressed and how it will affect performance of superconducting quantum interference devices (SQUIDs) and digital electronics circuits.As a solution for low-capacitance junctions, we propose a weak link made of an amorphous-silicon interlayer doped with nanoscale metallic drops between the two superconducting Mo-Re-alloy electrodes.
Superconducting quantum interference devices (SQUIDs) are promising for detection of extremely weak power regimes for the Internet of Things and long-distance satellite networks. In low-frequency magnetic signal measurements, it has demonstrated superior performance over the traditional systems. We review the resistively and capacitively shunted junction model of dc SQUIDs and investigate its transfer function to magnetic flux signals while taking thermal fluctuation into account. We numerically evaluate the influence of bias current and bias flux signal to determine the operating parameters of the device. The performances related to SQUID ring inductance operating at 4.2 K and 77 K are demonstrated. Combined with common radio frequency front-end modules, including low-noise amplifier and low-pass filter, we evaluate the bit-error-rate performance of the system under different inductance values and inferred that the sensitivity of the system can reach −99 dBm at 100 MHz bandwidth.