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Electronics Letters

SPICE model implementation of quantum phase‐slip junctions

Uday S. Goteti, Michael C. Hamilton

Published Jun 1, 2015• 15 citations
Publisher

Abstract

Quantum phase‐slips, which are the exact duals of Josephson junctions (JJs), are promising for several applications in classical and quantum superconducting electronic circuits. The experimental testing of the phase‐slip phenomena and identifying these applications has been challenging. In this reported work, the use of a dual to a JJ model to implement a SPICE model of a quantum phase‐slip junction (QPSJ) in JSPICE3, in order to explore possible circuit applications, is demonstrated. A transient analysis model of the device is presented and an example of an I–V curve simulation of the device, along with a simulation of a possible circuit application of the device, are also shown.

DOI
10.1049/el.2015.0904

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Quantum phase‐slips, which are the exact duals of Josephson junctions (JJs), are promising for several applications in classical and quantum superconducting electronic circuits. The experimental testing of the phase‐slip phenomena and identifying these applications has been challenging. In this reported work, the use of a dual to a JJ model to implement a SPICE model of a quantum phase‐slip junction (QPSJ) in JSPICE3, in order to explore possible circuit applications, is demonstrated. A transient analysis model of the device is presented and an example of an I–V curve simulation of the device, along with a simulation of a possible circuit application of the device, are also shown.
Superconducting circuits that operate by propagation of small voltage or current pulses, corresponding to propagation of single flux or charge quantum, are naturally suited for implementing spiking neuron circuits. Quantum phase-slip junctions (QPSJs) are 1-D superconducting nanowires that have been identified as exact duals to Josephson junctions, based on charge-flux duality in Maxwell’s equations. In this paper, a superconducting quantized-charge circuit element, formed using quantum phase-slip junctions, is investigated for use in high-speed, low-energy superconducting spiking neuron circuits. By means of a SPICE model developed for QPSJs, operation of this superconducting circuit to produce and transport quantized charge pulses, in the form of current pulses, is demonstrated. The resulting quantized-charge-based operation emulates spiking neuron circuits for brain-inspired neuromorphic applications. Additionally, to further demonstrate the operation of QPSJ-based neuron circuits, a QPSJ-based integrate and fire neuron circuit is introduced, along with simulation results using WRSPICE. Estimates for operating speed and power dissipation are provided and compared to Josephson junction and CMOS-based spiking neuron circuits. Current challenges are also briefly mentioned.
Superconducting digital computing systems, primarily involving Josephson junctions are actively being pursued as high performance and low energy dissipating alternatives to CMOS-based technologies for petascale and exascale computers, although several challenges still exist in overcoming barriers to practically implement these technologies. In this paper, we present an alternative superconducting logic structure: quantized charge-based logic circuits using quantum phase-slip junctions, which have been identified as dual devices to Josephson junctions. Basic principles of logic implementation using quantum phase-slips are presented in simulations with the help of a SPICE model that has been developed for the quantum phase-slip structures. Circuit elements that form the building blocks for complex logic circuit design are introduced. Two different logic gate designs: or gate and xor gate are presented to demonstrate the usage of the building blocks introduced.
The Josephson effect, tunnelling of a supercurrent through a thin insulator layer between two superconducting islands, is a phenomena characterized by a spatially distributed phase of the superconducting condensate. In recent years, there has been a growing focus on Josephson junction devices particularly for the applications of quantum metrology and superconducting qubits. In this study, we report the development of Josephson junction circuit formed by serially connecting many Superconducting Quantum Interference Devices, SQUIDs. We present experimental measurements as well as numerical simulations of a phase-slip center, a SQUID with weaker junctions, embedded in a Josephson junction chain. The DC transport properties of the chain are the result of phase slips which we simulate using a classical model that includes linear external damping, terminating impedance, as well as internal nonlinear quasiparticle damping. We find good agreement between the simulated and the experimental current voltage characteristics. The simulations allow us to examine the spatial and temporal distribution of phase-slip events occurring across the chains and also the existence of travelling voltage pulses which reflect at the chain edges.
Superconducting Josephson junctions and quantum phase slip (QPS) junctions create various hybrid circuits combined with nonsuperconducting elements. Those circuits require a common analysis method to bridge the gap between superconducting and nonsuperconducting electronics. This article presents an electromagnetic-flux-distribution model to unify the analyses of superconducting and non-superconducting circuits. This model uses electric and magnetic fluxes as the variables to unify the definitions of circuit elements and circuit laws; it derives general circuit equations of the circuits viewed from both electric and magnetic fields, to depict their dynamics and duality principles. This method is demonstrated in the analyses of a Josephson junction circuit and its dual QPS junction circuit. It shows that Josephson junction circuits are the magnetic-flux distribution network tuned by the Josephson current, while QPS junction circuits are the electric-flux distribution network modulated by the QPS voltage.
We consider the dynamics of a quantum phase-slip junction (QPSJ), a dual Josephson junction, connected to a microwave source with frequency ${\ensuremath{\omega}}_{\mathrm{mw}}$. With respect to an ordinary Josephson junction, a QPSJ can sustain dual Shapiro steps, consisting of well-defined current plateaus at multiple integers of $e{\ensuremath{\omega}}_{\mathrm{mw}}/\ensuremath{\pi}$ in the current-voltage $(I\text{\ensuremath{-}}V)$ characteristic. The experimental observation of these plateaus has been elusive up to now. We argue that thermal as well as quantum fluctuations can smear the $I\text{\ensuremath{-}}V$ characteristic considerably. In order to understand these effects, we study a current-biased QPSJ under microwave irradiation and connected to an inductive and resistive environment. We find that the effect of the fluctuations is governed by the resistance of the environment and by the ratio of the phase-slip energy and the inductive energy. Our results are of interest for experiments aiming at the observation of dual Shapiro steps in QPSJ devices for the definition of a new quantum current standard.
The phenomenon of coherent quantum phase-slips (CQPS) in superconducting nanowires was some time ago proposed to be the exact dual of the Josephson effect, a proposal accompanied by predictions of a new quantum current standard dual to the Josephson voltage standard. Unambiguous experimental observation of CQPS in nanowire structures has only recently been achieved through microwave spectroscopy which showed an avoided crossing between flux states for a superconducting ring interrupted by a superconducting nanowire. This observation raises expectations that the CQPS quantum current standard and a slew of CQPS devices dual to devices containing Josephson junction might be realised, including a tunable capacitance, a sensitive charge detector and small-signal detector. To date, experimental evidence for CQPS in a dc transport geometry has not been considered conclusive, and the impact of decoherence in CQPS devices still remains to be evaluated. We present experimental work which has enabled us to crystallise pertinent issues which have prevented the realisation of CQPS in dc transport experiments to date.