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Journal of Applied Physics

Response times of short Josephson junction and applications to rf SQUID’s

Eshel Ben‐Jacob, Y. Imry

Published Aug 1, 1980• 14 citations
Publisher

Abstract

The dynamics of a small Josephson junction, driven either by a current source or by an external flux when the junction is the weak link element of a SQUID ring, were studied. Approximate analytical arguments and numerical simulations were used for the lumped circuit model of the junction. The various characteristic times of these devices were systematically obtained as functions of the parameters G and K of the junction and of the SQUID, respectively. The forms of the flux transitions and the times governing them are obtained for linear and periodic time variations of the external flux on the SQUID. A coupling of the SQUID to an LC circuit was treated. Limitations on the device parameters consistent with fast response, stability, and sensitivity were obtained both for the current driven junction and for the rf SQUID.

DOI
10.1063/1.328251

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The dynamics of a small Josephson junction, driven either by a current source or by an external flux when the junction is the weak link element of a SQUID ring, were studied. Approximate analytical arguments and numerical simulations were used for the lumped circuit model of the junction. The various characteristic times of these devices were systematically obtained as functions of the parameters G and K of the junction and of the SQUID, respectively. The forms of the flux transitions and the times governing them are obtained for linear and periodic time variations of the external flux on the SQUID. A coupling of the SQUID to an LC circuit was treated. Limitations on the device parameters consistent with fast response, stability, and sensitivity were obtained both for the current driven junction and for the rf SQUID.
The dynamics of two inductively-coupled Josephson junctions, driven by a current source and by an external flux were studied. Approximate analytical arguments and numerical simulations were used. The various characteristics times of the DC-SQUID were systematically obtained as functions of the parameters of the junctions and the superconducting loop. We have studied the effects of the external magnetic field and quasiparticle conductance on the structure of the I-V characteristics. The transition times between the various branches of the I-V characteristics were calculated using approximate analytical arguments as well as numerical simulations. The results, both for the I-V characteristics and the transition times, were compared with existing experiments.
The equivalent parameters of a Josephson junction in a microwave SQUID structure are calculated on the basis of relations obtained as a result of an analysis of the operation of an rf SQUID. This analysis is based on the sawtooth variation of the voltage on the resonator as a function of the constant flux bias. The quantitative characteristics permit regarding the Josephson junction as a linear impedance in the rf or microwave circuit, whose real and imaginary parts are controlled by the constant magnetic flux passing through the SQUID loop.
The electrical equations of a resonant circuit fed with a radio-frequency current and inductively coupled to a weakly superconducting loop have been derived. The current-voltage characteristic of the rf superconducting quantum interference device can then be calculated and studied as a function of the junction resistance or of the resonance frequency, enabling its behavior to be better understood. As shown by Kurkijärvi, the large positive slope of the steps and the rounding of the characteristic result from thermal noise. However, in order to explain quantitatively the experimental results concerning, namely, point contact weak links which are generally oxidized or which have several contact points, it is useful to remark that the connection between the two superconductors constituting the Josephson junction may be made from n resistive paths. The mean thermal energy of the fluctuating flux is then close to nkbT instead of kbT if the inductances linking the contact points are large enough, that is, on the order of 10−11 H.
Abstract We consider, for the first time, the effects of strong capacitive and inductive coupling between radio frequency superconducting quantum interference devices (rf SQUIDs) in an overlapping metamaterial geometry when driven by rf flux at and near their self-resonant frequencies. The equations of motion for the gauge-invariant phases on the Josephson junctions in each SQUID are set up and solved. Our model accounts for the high-frequency displacement currents through capacitive overlap between the wiring of SQUID loops. We begin by modeling two overlapping SQUIDs and studying the response in both the linear and nonlinear high-frequency driving limits. By exploring a sequence of more and more complicated arrays, the formalism is eventually extended to the N × N × 2 overlapping metamaterial array, where we develop an understanding of the many ( 8 N 2 − 8 N + 3 ) resulting resonant modes in terms of three classes of resonances. The capacitive coupling gives rise to qualitatively new self-resonant responses of rf SQUID metamaterials, and is demonstrated through analytical theory, numerical modeling, and experiment in the 10–30 GHz range on capacitively and inductively coupled rf SQUID metamaterials.
We present numerical investigation of the RF properties of a double-junction SQUID model, which is referred to as an RF-field-driven double-junction SQUID (RFDS). The RFDS generates large current steps, the order of which can be controlled by external dc field. We simulate the current-voltage characteristics of the RFDS in the normalized frequency range from 0.065 to 5.0. In comparison with the results for a single junction, the step heights of the RFDS are much larger for the low frequency region; e.g. the first step of the RFDS becomes nine times larger than that of a single junction when a dc flux of 0.5 0 is applied ( 0 is a flux quantum). For the high frequency region, the step height of the RFDS is comparable to that of a single junction. The results suggest that the RFDS should be applicable as a wide-band RF detector.