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Review of Scientific Instruments

Accurate periodicity measurement of superconducting quantum interference device magnetic flux response

Masakazu Nakanishi

Published Sep 1, 2010• 2 citations
Publisher

Abstract

It is theoretically explained that a response of a superconducting quantum interference device (SQUID) is periodically dependent on total magnetic flux coupling to the SQUID ring (Φ) and its period is a flux quantum (Φ(o)=h/2e, where h and e, respectively, express Planck's constant and elementary charge). For example, the voltage of an electromagnetically oscillated rf-SQUID or a current biased dc-SQUID is thought to be periodically dependent on Φ with a period of Φ(o). In this paper, we propose an accurate method to check the periodicity of a SQUID response by using a set of sensing coils covered with a superconducting sheath. As a demonstration, we measured periodicity of a commercially available thin-film type rf-SQUID response in magnetic flux ranging up to approximately 4300Φ(o). Its flux dependence was periodic below about 3400Φ(o).

DOI
10.1063/1.3483261

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Chinese Physics B•Sep 1, 2012•4 citations
It is theoretically explained that a response of a superconducting quantum interference device (SQUID) is periodically dependent on total magnetic flux coupling to the SQUID ring (Φ) and its period is a flux quantum (Φ(o)=h/2e, where h and e, respectively, express Planck's constant and elementary charge). For example, the voltage of an electromagnetically oscillated rf-SQUID or a current biased dc-SQUID is thought to be periodically dependent on Φ with a period of Φ(o). In this paper, we propose an accurate method to check the periodicity of a SQUID response by using a set of sensing coils covered with a superconducting sheath. As a demonstration, we measured periodicity of a commercially available thin-film type rf-SQUID response in magnetic flux ranging up to approximately 4300Φ(o). Its flux dependence was periodic below about 3400Φ(o).
We developed a digital-to-analog converter (DAC) having a current output and incorporating a superconducting quantum interference device (SQUID). The linearity of the device is based on the periodic dependence of the SQUID response on the magnetic flux coupling to the SQUID ring. The period is a flux quantum (Φ(o) = h/2e, where h is Planck's constant and e is the elementary charge). Because of the device's quantum accuracy, the output is essentially linear. The SQUID DAC was constructed using a commercially available rf-SQUID, the periodicity of which has been experimentally verified below 3420 Φ(o). An adjustable number of current amplitudes are dependent on maximum output (I(max)). The output current is adjustable to ~100 000 different values when I(max) ~1 mA and ~1,000,000 when I(max) ~0.1 mA. The short-term fluctuation of ~0.15 ppm was attributable to flux resolution of the SQUID. As a demonstration, measurements showing the voltage linearity of a digital multimeter were performed.
Responses of a superconducting quantum interference device (SQUID) are periodically dependent on magnetic flux coupling to its superconducting ring and the period is a flux quantum (Φo = h/2e, where h and e, respectively, express Planck's constant and elementary charge). Using this periodicity, we had proposed a digital to analog converter using a SQUID (SQUID DAC) of first generation with linear current output, interval of which corresponded to Φo. Modification for increasing dynamic range by interpolating within each interval is reported. Linearity of the interpolation was also based on the quantum periodicity. A SQUID DAC with dynamic range of about 1.4 × 10(7) was created as a demonstration.
At an extremely low temperature of 20 mK, we measured the loop current in a tunable rf superconducting quantum interference device (SQUID) with a dc-SQUID. By adjusting the magnetic flux applied to the rf-SQUID loop (Φ f ) and the small dc-SQUID (Φ cjj f ), respectively, the potential shape of the system can be fully controlled in situ. Variation in the transition step and overlap size in the switching current with a barrier flux bias are analyzed, from which we can obtain some relevant device parameters and build a model to explain the experimental phenomenon.
The response of a double hole RF SQUID to modulation by magnetic flux phi e introduced into one of the holes is first considered. The output voltage v 0 is a periodic function of phi e but it is shown that one would expect the period not to be equal to the flux quantum phi 0 itself but to some multiple of it. The flux in either hole of the SQUID may be calculated by imagining the weak link broken and the RF drive removed: one period of the v 0 variation is produced by a change in phi e sufficient to change the flux in either hole (averaged over one RF cycle), due both to current in the coil and to current induced on the inside wall of the SQUID, by phi 0 . This principle is applied to a double hole SQUID modified by the replacement of part of one wall by a block of normal metal (an R SQUID). Explicit expressions for the response to modulation, which is frequency dependent, are derived in the limit of low frequency, and more generally, at any frequency, for an R SQUID in which both the holes and the modulation coil are long in comparison with their diameter. The size of the superconducting screen which must surround the R SQUID, if only to avoid interference from other magnetic fields in the laboratory, is shown to play an important part in determining the response at low frequencies. The spectrum of noise currents is also calculated.
We present a theoretical study on the voltage response function 〈V〉 of series arrays of dc superconducting quantum interference devices (SQUIDs) for which the elementary dc SQUID loops vary in size and, possibly, in orientation. If the distribution of the array loop sizes is chosen according to an arithmetic relation, 〈V〉 is not a Φ0-periodic function of the strength of external magnetic field B. For arithmetic arrays the periodicity of 〈V〉 is controlled by the geometry of the array alone and does not depend on spreads in the array junction parameters. If small fluctuations are added to the loop size distribution, 〈V〉 becomes a unique function around a global minimum at B=0 without possessing significant additional minima for finite B. This filter property does not apply for conventional SQUIDs and series arrays of identical or nearly identical SQUID loops. Applications of arithmetic series arrays include the design of current amplifiers and novel quantum interference filters, which possess large voltage swing and low noise level. In particular, quantum interference filters should provide a rather simple and extremely sensitive measurement of the absolute strength of magnetic fields.
At an extremely low temperature of 20 mK, we measured the loop current in a tunable rf superconducting quantum interference device (SQUID) with a dc-SQUID. By adjusting the magnetic flux applied to the rf-SQUID loop ( Φ f ) and the small dc-SQUID ( Φ f cjj ), respectively, the potential shape of the system can be fully controlled in situ . Variation in the transition step and overlap size in the switching current with a barrier flux bias are analyzed, from which we can obtain some relevant device parameters and build a model to explain the experimental phenomenon.