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IEEE Transactions on Applied Superconductivity

Resonances and Phase Locking in Josephson High-Q Circuit

Victor K. Kornev, Nikolay V. Kolotinskiy

Published Mar 22, 2018• 2 citations
Publisher

Abstract

We consider Josephson junction coupled to a high-quality tank circuit and present both analytic analyses and numerical simulation results for resonances of both force and parametric types as well as Shapiro steps under microwave irradiation with frequency close to the resonance one. Physical mechanisms of the phenomena are studied and discussed.

DOI
10.1109/tasc.2018.2817366

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•Jan 1, 2006•0 citations
We consider Josephson junction coupled to a high-quality tank circuit and present both analytic analyses and numerical simulation results for resonances of both force and parametric types as well as Shapiro steps under microwave irradiation with frequency close to the resonance one. Physical mechanisms of the phenomena are studied and discussed.
We consider a Josephson junction coupled to a high-quality parallel resonance circuit under microwave irradiation on the resonance frequency. The phase locking of Josephson oscillations, manifesting itself through Shapiro steps, is studied using an analytical theory developed for the circuit. Substantial change in the amplitude of the oscillating component of the Josephson phase within the phase-locking range determines specificity of the step behavior. This analysis is compared with the results of a numerical simulation.
We study an effect of external radiation on the dynamics of Josephson junction shunted by an LC circuit. When the Josephson frequency is equal to the frequency of the circuit, additional stable resonant circuit branches appear in the IV -characteristic of the junction. The branches occur on the stable side of a narrow resonance peak, while the other peak side has a negative slope and is unstable. We show that the amplitude dependence of the Shapiro step width crucially changes when the Shapiro step is on the resonant circuit branch. These effects might give very important advantages for methods and technologies that exploit the response of Josephson junctions to microwave fields.
Results on analytical and computational investigations of high frequency dynamics of Josephson junctions, characterized by nonzero capacitance and the second harmonic in the current-phase relation are presented. These attributes each influence on behaviour of integer Shapiro steps and lead to formation of non-integer Shapiro steps. Analytic theory of the integer and non-integer Shapiro steps has been developed for so-called high frequency limit. The analytical and numerical results are compared with experimental data for hybrid heterostructures YBCO/Au/Nb. Detector response for the case of high fluctuation level has been considered as well.
A high temperature superconducting YBa2Cu3Oy array of five Josephson junctions designed with additional coupling lines has been developed to demonstrate the effects of frequency locking and impedance matching for applications such as oscillators, mixers, and detectors. The Josephson self-radiation power was directly detected by a superheterodyne receiver, and Shapiro steps were also measured. The Josephson self-radiation properties reveal good quality of phase locking and microwave coupling with external circuits. The maximum self-radiation power of our array is about 50 pW which is several ten times higher than that of a single Josephson junction, and its peak point exactly satisfies the Josephson current-voltage relation. The Shapiro-step measurements show that the behavior of current-voltage curve depends on the effective inductance of coupling lines which affects the total impedance of Josephson junction array and microwave coupling. The Josephson oscillation frequency was obtained up to about 880 GHz which is 73% of the maximum available frequency calculated from the characteristic voltage of the Josephson junctions. Experimental results show that this type of Josephson junction array can improve the Josephson self-radiation power and increase the maximum detectable frequency.
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.
We describe a variety of models to characterize the behavior of several types of underdamped Josephson systems.We also present numerical results based on these models.We first discuss a stack of small junctions in a single mode resonant cavity.Such a stack is believed to be appropriate to model some high temperature cuprate superconductors such as Bi 2 Sr 2 CaCu 2 O 8+x .Our results show self-induced-resonant-steps in the current voltage (IV) curve.These steps represent a coherent phase locking between the junctions in the stack and the resonant cavity.Next we generalize these results to treat a single long junction coupled to a single mode resonant cavity.We find a number of features not seen in stacks of small junctions.Our numerical results show that if the electromagnetic fields of the cavity mode are spatially periodic, we again see steps in the IV curve and furthermore, for sufficiently large coupling, the cavity frequency is shifted by coupling to the long junction.We also discuss how a stack of long junctions could be used to model a layered high temperature superconductor.We then turn to some properties of single junctions in the "quantum" regime where the phase/number non-commutation is important.This quantum regime is crucial to all proposals to use such junctions as solid state quantum bits (qubits).We show that such qubits, when subjected to external a.c.perturbations, exhibit not only . . . . . . . . . .