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Journal of Applied Physics

Dynamics of the DC-SQUID

Eshel Ben‐Jacob, Y. Imry

Published Nov 1, 1981• 29 citations
Publisher

Abstract

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.

DOI
10.1063/1.328634

Related papers

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

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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 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.
This paper describes the I-V characteristics (as a function of applied magnetic field) and magnetic field response of a dc SQUID which incorporates two weak-link Josephson junctions in a superconducting ring. These characteristics are derived by digital computer simulation, using the Stewart-McCumber model. The effects of asymmetry (dissimilarity between the junctions) on SQUID critical current I c, normal resistance R and capacitance C are also simulated. With microwave excitation applied, the Josephson oscillations of the dc SQUID are found to be “frequency-locked” to the applied microwave signal even when critical currents I c of the two junctions differed, Subharmonic voltage steps are obtained for a symmetric dc SQUID in a magnetic field even when the current-phase relationship is purely sinusoidal.
We present an improved analytic theory, numerical simulation, and analysis of noise characteristics of a bi-SQUID in comparison with those of a dc SQUID in an open loop configuration. The analytic theory which had been developed earlier, neglecting a pulse component of the difference of the phases of Josephson junctions, is now completed taking into account the pulse component. In the bi-SQUID, the additional Josephson junction introduces another source of fluctuations and changes its transfer function, nonlinear dynamics, and the noise spectrum transformation. Some increase in the reduced-to-input noise at low values of applied magnetic flux comes from the nonlinear flux to phase difference transformation that was introduced in bi-SQUID as a way to linearize its voltage response.
We study a 0-$\ensuremath{\pi}$ dc superconducting quantum interference device (SQUID) with asymmetric inductances and critical currents of the two Josephson junctions (JJs). By considering such a dc SQUID as a black box with two terminals, we calculate its effective current-phase relation ${I}_{s}(\ensuremath{\psi})$ and the Josephson energy $U(\ensuremath{\psi})$, where $\ensuremath{\psi}$ is the Josephson phase across the terminals. We show that there is a domain of parameters where the black box has the properties of a $\ensuremath{\varphi}$ JJ with degenerate ground state phases $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The $\ensuremath{\varphi}$ domain is rather large, so one can easily construct a $\ensuremath{\varphi}$ JJ experimentally. We derive the current phase relation and show that it can be tuned in situ by applying an external magnetic flux resulting in a continuous transition between the systems with static solutions $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi},\phantom{\rule{0.16em}{0ex}}\ensuremath{\psi}={\ensuremath{\varphi}}_{0} ({\ensuremath{\varphi}}_{0}\ensuremath{\ne}0,\ensuremath{\pi})$ and even $\ensuremath{\psi}={\ensuremath{\varphi}}_{0}\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The dependence of ${\ensuremath{\varphi}}_{0}$ on applied magnetic flux is not $2\ensuremath{\pi}$ (one flux quantum) periodic.
The experimental results obtained with low noise dc superconducting quantum interference devices (dc-SQUIDs) are sometimes not well understood. In particular, when the critical current is high, very irregular voltage versus flux characteristics can be measured. On the other hand, when the critical current is low, the characteristics follow perfectly the resistively shunted junction model. We have studied the dynamics of a dc-SQUID in the presence of stray capacitance and shunting resistors imbalance. The equations describing a circuit model for this physical system are integrated numerically and the results are compared with voltage versus flux characteristics obtained from fabricated devices. We find that the theoretical analysis accounts very well for previously misunderstood experimental features of the dc-SQUID. This model can give more physical sense to the various regimes of behavior of the dc-SQUID giving more insight into the experimental results.