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IEEE Transactions on Magnetics

Current-phase relations and noise in rf biased squids

L. D. Jackel, Terrence D. Clark, Robert A. Buhrman

Published Mar 1, 1975• 7 citations
Publisher

Abstract

An investigation has been made of the effect of the weak link current-phase relation on noise in rf biased SQUIDs. Non-sinusoidal current-phase relations have been observed in various weak links and these non-sinusoidal relations have been correlated with significantly increased intrinsic noise in the SQUID ring. The current-phase relation is also found to affect the amplitude of the rf SQUID ring dissipation. The result of a rf SQUID system noise analysis shows that, due to increased intrinsic noise and reduced ring dissipation, the minimum attainable noise for a SQUID ring having a very non-sinusoidal current-phase relation is considably greater than for a ring with a sinusoidal relation.

DOI
10.1109/tmag.1975.1058695

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Journal of Applied Physics•May 1, 1994•26 citations
An investigation has been made of the effect of the weak link current-phase relation on noise in rf biased SQUIDs. Non-sinusoidal current-phase relations have been observed in various weak links and these non-sinusoidal relations have been correlated with significantly increased intrinsic noise in the SQUID ring. The current-phase relation is also found to affect the amplitude of the rf SQUID ring dissipation. The result of a rf SQUID system noise analysis shows that, due to increased intrinsic noise and reduced ring dissipation, the minimum attainable noise for a SQUID ring having a very non-sinusoidal current-phase relation is considably greater than for a ring with a sinusoidal relation.
An investigation has been made of the effect of the weak link current-phase relation on noise in rf biased SQUIDs. Non-sinusoidal current-phase relations have been observed in various weak links and these non-sinusoidal relations have been correlated with significantly increased intrinsic noise in the SQUID ring. The current-phase relation is also found to affect the amplitude of the rf SQUID ring dissipation. The result of a rf SQUID system noise analysis shows that, due to increased intrinsic noise and reduced ring dissipation, the minimum attainable noise for a SQUID ring having a very non-sinusoidal current-phase relation is considably greater than for a ring with a sinusoidal relation.
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.
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)
SQUIDs employing short (\sim 1 \mu) ultra thin weak link sections of "granular" niobium and niobium nitride have been prepared on cylindrical quartz substrates by rf and rf reactive sputtering, photolithography and anodization. These SQUIDs have demonstrated near ideal intrinsic noise characteristics when biased at 20 MHz. Niobium nitride devices have operated with this nearly intrinsic noise at temperatures up to 12.5 K. Current-phase relation and flux entry versus applied flux were measured on one niobium SQUID. Results indicate a nearly [if not exactly] sinusoidal current-phase relation from Tcto almost a degree below Tcand flux entry noise in good agreement with the intrinsic flux noise theory. Biasing these devices at 9.2 GHz gives a degraded response which can be related to relaxation effects in the weak links. Thermal noise switching between the superconducting and dissipative states was also observed at 9.2 GHz and could be fit by a simple model.
A detailed study has been made of the low-frequency excess noise of rf superconducting quantum interference devices (SQUIDs), fabricated from thin niobium films and operated at 4.2 K, with rf bias frequencies of 0.15, 1.7, and 3 GHz. When the SQUIDs were operated in an open-loop configuration in the absence of low-frequency flux modulation, the demodulated rf voltage exhibited a substantial level 1/f noise, which was essentially independent of the rf bias frequency. As the rf bias frequency was increased, the crossover frequency at which the 1/f noise power was equal to the white noise power moved to higher frequencies, because of the reduction in white noise. On the other hand, when the SQUID was flux modulated at 50 kHz and operated in a flux locked loop, no 1/f noise was observed at frequencies above 0.5 Hz. A detailed description of how the combination of rf bias and flux modulation removes 1/f noise due to critical current fluctuations is given. Thus, the results demonstrate that the 1/f noise observed in these SQUIDs is generated by critical current fluctuations, rather than by the hopping of flux vortices in the niobium films.