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Japanese Journal of Applied Physics

Precision improvement of the current multiplier based on the quantum current-mirror effect

Kouichi Takeda, Chihiro Ishida, Srinivas Gandrothula, Yoshinao Mizugaki, Hiroshi Shimada

Published Jan 23, 2014• 0 citations
Publisher

Abstract

The relationship between the coupling strength and the uncertainty in current duplication was investigated for the quantum current-mirror effect in capacitively coupled arrays of small Josephson junctions. With the increase in the coupling factor κ, defined as , with C c being the coupling capacitance and C the capacitance of the junction, the uncertainty decreased rapidly, especially at , and the standard deviation of the error reached as low as the order of 10 fA at . On this basis, we fabricated a 10-fold current multiplier composed of 11 simple arrays of junctions coupled more strongly ( ), using a plate-capacitor structure, than a previously studied multiplier ( ). It demonstrated more precise current-multiplication behavior than the previous multiplier with no intentional coupling structure, and the standard deviation of the error in current multiplication was decreased to less than 1/10 of the previous result.

DOI
10.7567/jjap.53.023101

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The relationship between the coupling strength and the uncertainty in current duplication was investigated for the quantum current-mirror effect in capacitively coupled arrays of small Josephson junctions. With the increase in the coupling factor κ, defined as , with C c being the coupling capacitance and C the capacitance of the junction, the uncertainty decreased rapidly, especially at , and the standard deviation of the error reached as low as the order of 10 fA at . On this basis, we fabricated a 10-fold current multiplier composed of 11 simple arrays of junctions coupled more strongly ( ), using a plate-capacitor structure, than a previously studied multiplier ( ). It demonstrated more precise current-multiplication behavior than the previous multiplier with no intentional coupling structure, and the standard deviation of the error in current multiplication was decreased to less than 1/10 of the previous result.
We report our observation of a current-multiplication trend in a new class of current-multiplier designs based on the quantum current-mirror effect in coupled arrays of small Josephson junctions. We demonstrate an extension of the current doubler device to 8- and 10-fold current multipliers by including additional Josephson junction arrays with simplified device geometry. The devices showed the expected current-multiplication trend at low temperatures where the charging effect was dominant. The magnitude of the current that exhibited such a multiplication trend was as large as 0.8 nA.
Two types of current doublers, which operate in a sub-nanoampere range, have been fabricated as prototypes of a precise current multiplier for metrological application. The current doubling function of the devices is based on the quantum current-mirror effect in coupled arrays of small Josephson junctions. Both types of devices comprise three arrays of small Josephson junctions: the first device has two serial short arrays coupled to one long array, and the second device has three arrays of the same size arranged in parallel. The arrays for the current input are the long array in the first device and one of the three arrays in the second device, and a parallel connection of the other two arrays in each device forms the output port. In both types of devices, a current fed to the input array is doubled in the output circuit, which includes the connected arrays, up to about 100 pA with the accuracy ≤±3 pA, which is the uncertainty of the measurement system, by correlated tunnelings of Cooper-pair charge solitons in the arrays. The feasibility of producing a current multiplier has been ascertained on the basis of this effect.
A Josephson single-flux-quantum voltage/frequency multiplier circuit is proposed as the basic building block for a new generation of voltage standards. The circuit uses magnetic coupling to synchronize a series array of independent junction oscillators to the flux flow in a Josephson transmission line. A cascade of these circuits can multiply an arbitrarily low input frequency up to the frequency limit of the circuit ( approximately=250 GHz) and then add the voltages across approximately 30000 oscillators to generate precise voltages up to 10 V. Because the oscillators can be switched on and off with a bias current, the output voltage is rapidly programmable. A complete design for a voltage standard programmable in 1.2- mu V increments to a maximum of 10 V is proposed. Using existing fabrication technology, the circuit would cover a substrate area of about 1 cm/sup 2/ and use 67210 junctions.>
New types of followers and follower/doublers of DC voltage are proposed and analyzed. Operation of the devices is based on synchronization of the single-flux quantum (SFQ) pulses generated by overdamped Josephson junctions coupled by means of passive capacitive or inductive circuits. Two ways of combining the followers and doublers to get DC voltage multipliers and standards are described. Possible applications of these devices in A/D and D/A converters and RSFQ (rapid SFQ) logic circuits are also discussed. It is believed that the proposed multipliers and standards could produce stable output voltages in the 1-10 V range with output currents in the 0.1-1 mA range.>
We have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures (T=0.02−−0.6K),(T=0.02--0.6\mathrm{K}),(T=0.02−−0.6K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction $I\ensuremath{-}V$ curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance ${R}_{0}^{\ensuremath{'}}$ of the SQUID arrays is much higher than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega}.$ The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the $I\ensuremath{-}V$ curves numerically in order to compare then with the experimental ones at ${R}_{0}^{\ensuremath{'}}\ensuremath{\gg}{R}_{K}.$ The numerical calculation agrees with the experiments qualitatively. We also discuss the ${R}_{0}^{\ensuremath{'}}$ dependence of the single-Josephson-junction $I\ensuremath{-}V$ curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.
Rapid-single-flux-quantum digital-to-analogue converters (RSFQ-DACs) are now under development for ac voltage standard applications. The voltage multiplier (VM), which precisely amplifies the input voltage, is a key component for RSFQ-DACs. Because the amount of bias current for a conventional VM increases in proportion to its multiplication factor, we have been looking for a VM device which is operated on a different principle. In this paper, we report our design of a 1000-fold VM comprising double flux quantum amplifiers (DFQAs) of which the amount of bias current is independent of its multiplication factor. Test circuits were fabricated using a 2.5 kA/cm2 Nb process. We confirm that the experimental results demonstrate the 1000-fold operation up to 13.2 GHz input SFQ pulse repetition frequency.