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Japanese Journal of Applied Physics

Current Multiplication Using Arrays of Small Josephson Junctions

Srinivas Gandrothula, Kenta Nakamura, Masashi Takiguchi, Yoshinao Mizugaki, Hiroshi Shimada

Published Nov 16, 2012• 1 citation
Publisher

Abstract

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.

DOI
10.1143/jjap.51.123101

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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.
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.
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We present observations of charging effects for Cooper pairs in short linear arrays of small-capacitance Josephson junctions. Current-voltage characteristics show a Coulomb gap for Cooper-pair tunneling when the charging energy exceeds the Josephson coupling energy. In a double junction a zero-voltage current is observed that is modulated by a gate voltage applied to the metal island between the junctions. For longer arrays a crossover from Coulomb blockade of Cooper-pair tunneling to a supercurrent is observed when the ratio of Josephson coupling to charging energy is increased.
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.
The growing market for fast floating-point coprocessors, digital signal processing chips, and graphics processors has created a demand for high speed, area efficient multipliers. Current architectures range from small, low-performance shift and add multipliers, to large, high-performance array and tree multipliers. Conventional linear array multipliers achieve high performance in a regular structure, but require large amounts of silicon. Tree structures achieve even higher performance than linear arrays but the tree interconnection is more complex and less regular, making them even larger than linear arrays. Ideally, one would want the speed benefits of a tree structure, the regularity of an array multiplier, and the small size of a shift and add multiplier. In electronics, rapid single flux quantum (RSFQ) is a digital electronics technology that relies on quantum effects in superconducting devices, namely Josephson junctions, to process digital signals. Josephson junctions are the active elements for RSFQ electronics, just as transistors are the active elements for semiconductor electronics. However, RSFQ is not a quantum computing technology in the traditional sense. Even so, RSFQ is very different from the traditional CMOS transistor technology used in every day computers due to its power efficiency and high speed it is being used.