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Journal of Applied Physics

Noise in the superconducting quantum flux detector

J. Kurkijärvi

Published Aug 1, 1973• 83 citations
Publisher

Abstract

An expression is derived for noise in the tank circuit of a superconducting quantum flux detector run at a radiofrequency. This noise is limited by the sensing element of the device, the superconducting ring with a weak link, and is therefore intimately related to the thermal fluctuations in the ring. Not considering external noise, the superconducting ring and the tank circuit together with the preamplifier should exhaust the important sources of noise in the flux detector.

DOI
10.1063/1.1662830

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An expression is derived for noise in the tank circuit of a superconducting quantum flux detector run at a radiofrequency. This noise is limited by the sensing element of the device, the superconducting ring with a weak link, and is therefore intimately related to the thermal fluctuations in the ring. Not considering external noise, the superconducting ring and the tank circuit together with the preamplifier should exhaust the important sources of noise in the flux detector.
This paper presents the results of an extensive study of the sensitivity-limiting noise sources in rf-biased SQUID flux detectors. Our investigation has included both experiments with point contact and thin-film SQUIDs and digital computer simulations. The paper begins with a discussion of rf SQUID operation, with special emphasis on those aspects that determine flux detector sensitivity. We then discuss the origin and consequences of intrinsic device noise in rf SQUID systems. We describe a straightforward technique for determining intrinsic noise amplitude directly from SQUID rf I–V characteristics. Deviations in the measured intrinsic noise of many devices from the Kurkijarvi-Webb prediction are attributed to departures from the ideal Josephson sinusoidal current-phase relation in the SQUID weak link. Kurkijarvf's SQUID tank circuit noise analysis is reviewed and we show how SQUID sensitivity can be maximized by an optimal coupling between SQUID ring and tank circuit. This optimal coupling depends upon circuit parameters, ring inductance, and weak-link properties. The analysis reveals that variations in the current-phase relation can result in a difference of as much as a factor of ten in the attainable sensitivity of two otherwise identical SQUID systems. We also suggest efforts in circuit design that are most likely to lead to further improvements in flux detector sensitivity. Finally, other factors, including external magnetic noise and underdamping of the SQUID ring, are discussed.
We analyze the influence of noise on magnetic properties of a superconducting loop which contains three Josephson junctions. This circuit is a classical analog of a persistent current (flux) qubit. A loop supercurrent induced by external magnetic field in the presence of thermal fluctuations is calculated. To connect with experiment, we calculate the impedance of a low-frequency tank circuit which is inductively coupled with the loop of interest. We compare the results with the results obtained in the quantum mode — when the three junction loop exhibits quantum tunneling of the magnetic flux. We demonstrate that the tank–loop impedance in the classical and quantum modes have different temperature dependence and can be easily distinguished experimentally.
Based on the hypothesis that the macroscopic superconducting shielding current on the surface of a porous granular superconductor is short lived due to the action of thermal noise, a dispersive-mode theory for a high-temperature radio-frequency superconducting quantum interference device (rf SQUID) is suggested. In this theory, the effect of the SQUID ring on the resonant tank circuit is an effective inductance Le{L}_{e}Le​, Le{L}_{e}Le​=k2{k}^{2}k2FLT{\mathrm{FL}}_{T}FLT​, where k is the coupling coefficient between the SQUID ring and the resonant tank circuit with inductance LT{L}_{T}LT​, and F is a periodic function of external flux ${\ensuremath{\Phi}}_{\mathrm{dc}}$ with a period of flux quantum ${\ensuremath{\Phi}}_{0}$. The phenomena that the weak-link-rf-SQUID flux-receiving area defined by the hole of the SQUID ring and the bulk-rf-SQUID flux-receiving area, which is determined by an annular surface region with a thickness of the effective penetration depth ${\ensuremath{\lambda}}_{e}$, can be interpreted. The theory is qualitatively consistent with available experimental results.
A low noise radiofrequency amplifier (10), using a dc SQUID (superconducting quantum interference device) as the input amplifying element. The dc SQUID (11) and an input coil (12) are maintained at superconductivity temperatures in a superconducting shield (13), with the input coil (12) inductively coupled to the superconducting ring (17) of the dc SQUID (11). A radiofrequency signal from outside the shield (13) is applied to the input coil (12), and an amplified radiofrequency signal is developed across the dc SQUID ring (17) and transmitted to exteriorly of the shield (13). A power gain of 19.5.+-.0.5 dB has been achieved with a noise temperature of 1.0.+-.0.4 K. at a frequency of 100 MHz.
In this paper a discussion is given of the noise sources and sensitivity limits of the rf biased SQUID. Both the low critical current inductive and the higher critical current hysteretic devices are considered. The intrinsic SQUID noise is treated by considering the internal flux response of a SQUID ring to an applied rf flux. While approximate, this approach yields the most direct picture of the nature of the intrinsic noise. Circuit optimization procedures for maximizing SQUID performance under various operating conditions are also outlined. Finally the effects of non-ideal weak link behavior upon SQUID operation are treated. (Author)