Equivalent Single-Junction Model of Superconducting Quantum Interference Devices in the Presence of Time-Varying Fields

R De Luca

doi:10.5402/2011/724384

Abstract

The reduced dynamical model of a two-junction quantum interference device is generalized to the case of time-varying externally applied fluxes with a d. c. component and an oscillating addendum whose frequency is comparable with the inverse of the characteristic time for flux dynamics within the superconducting system. From the resulting effective single-junction model for null inductance of the superconducting loop, it can be seen that the critical current of the device shows a dependence on the frequency and amplitude of the oscillating part of the applied flux. It can therefore be argued that the latter quantities can be considered as control parameters in the voltage versus applied flux curves of superconducting quantum interference devices.

Highlights

It is well known that the electrodynamic properties of SQUIDs can be obtained by means of the dynamics of the Josephson junction(s) in the system [1,2,3]
The Josephson junction dynamics is described by means of a nonlinear first-order ordinary differential equation (ODE) written in terms of the phase variable φ, which is the average of the gauge-invariant superconducting phase differences, φ1 and φ2, across the two junctions in the SQUID
SQUID, in the present work, we consider the dynamics of the superconducting quantum interferometer in the presence of a time-varying applied magnetic flux, whose frequency ω is considered to be comparable with tL−1

Summary

Introduction

It is well known that the electrodynamic properties of SQUIDs (superconducting quantum interference devices) can be obtained by means of the dynamics of the Josephson junction(s) in the system [1,2,3]. SQUID takes the inductance L of a single branch of the device to be negligible, so that β = LIJ /Φ0 ≈ 0, where Φ0 is the elementary flux quantum and IJ is the average value of the maximum Josephson currents of the junctions In this way, the Josephson junction dynamics is described by means of a nonlinear first-order ordinary differential equation (ODE) written in terms of the phase variable φ, which is the average of the gauge-invariant superconducting phase differences, φ1 and φ2, across the two junctions in the SQUID. Equation (1) is similar to the nonlinear first-order ODE describing the dynamics of the gauge-invariant superconducting phase of a single overdamped JJ with maximum current IJF modulated in field (IJF = | cos πψex|) in which a normalized bias current iB/2 flows This strict equivalence comes from the hypothesis that the total normalized flux ψ = Φ/Φ0 linked to the interferometer loop can be taken to be equal to ψex. SQUID, in the present work, we consider the dynamics of the superconducting quantum interferometer in the presence of a time-varying applied magnetic flux, whose frequency ω is considered to be comparable with tL−1

SQUID Dynamics

Time Averaging the Rapid Variable

Conclusion