Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Superconductor Science and Technology

Analysis of the periodicity of voltage versus applied flux curves of planar and three-dimensional SQUIDs in the presence of coupling inhomogeneity

Roberto De Luca

Published Oct 23, 2009• 0 citations
Publisher

Abstract

Coupling inhomogeneities in the Josephson junctions of planar 0-SQUIDs and π-SQUIDs and of three-dimensional SQUIDs are considered. Starting from the properties of planar SQUIDs, it is shown that slight non-homogeneous couplings of the twelve junctions in three-dimensional superconducting interferometers do not affect the periodicity properties of voltage versus applied flux curves. The results are obtained by applying a rigorous and general analytic approach to planar and three-dimensional superconducting devices.

DOI
10.1088/0953-2048/22/12/125010

Related papers

Dynamic electromagnetic response of three-dimensional Josephson junction arrays

J. Oppenländer, Ch. Häussler, Nils Schopohl

We present a theoretical study on the dynamical properties of three-dimensional arrays of Josephson junctions. Our results indicate that such superconducting networks represent highly sensitive three-dimensional superconducting quantum interference devices (3D SQUIDs) having some major advantages in comparison with conventional planar SQUIDs. The voltage response function of 3D SQUIDs is directly related to the vector character of external electromagnetic fields. The theory developed here allows the three-dimensional reconstruction of a detected external field including phase information about the field variables. Applications include the design of magnetometers, gradiometers, and particle detectors.

arXiv:cond-mat/9907105•Journal of Applied Physics•Nov 15, 1999•12 citations

Effect of trapped magnetic flux on the threshold curves of three-junction superconducting quantum interference devices

Wen‐Hao Chang

Thin-film Josephson-junction quantum-interference devices require only a small amount of magnetic flux to switch them between the voltage state and the superconducting state. They are sensitive to any spurious magnetic flux present at the device. The magnetic flux may be trapped in the superconducting ground plane, particularly in ground plane holes. This paper analyzes the effects of the trapped magnetic flux on the threshold curves of three-junction Josephson interferometers. The threshold curves of the interferometer are calculated automatically by using a circuit optimization program. The automatic procedure of calculating the threshold curves of an interferometer can be applied to any Josephson-junction interferometer device. The threshold curves of both symmetric and asymmetric interferometers are calculated. We find that the threshold curves of a symmetric three-junction interferometer changes periodically as a function of the effective coupled trapped magnetic flux with a period of Φ0. The threshold curves are shifted and severely distorted in shape by the presence of the coupled trapped magnetic flux. The degeneracy of the threshold curves of a symmetric interferometer makes the unique quantitative determination of the trapped magnetic flux difficult. However, the degeneracy is removed in an asymmetric interferometer. The presence of the unbalanced trapped magnetic flux greatly shifts the entire threshold curve of an asymmetric interferometer.

Journal of Applied Physics•Dec 1, 1982•3 citations

Dynamic properties of a superconducting quantum interference device containing arrays of Josephson junctions

Marian Darula, P. Seidel, F. H. Busse +1 more

The dynamic properties of a superconducting quantum interference device (SQUID) containing arrays of Josephson junctions in a superconducting loop, and in particular the case of a four-junction SQUID, is analyzed theoretically via computer simulations. It is shown that phase locking of Josephson junctions determines the dynamic behavior of the SQUID. In the case of a stable phase-lock state hysteretic I-V curves as well as unusual voltage-flux dependencies appear. The influence of a small spread in the Josephson junction parameters upon the stability of the phase-lock state is investigated in parameter space.

Journal of Applied Physics•Aug 15, 1993•21 citations

Voltage versus Flux Relation of DC Superconducting Quantum Interference Device Using Three Josephson Junctions

Keiji Enpuku, Hideki Doi

It has been shown that the voltage versus flux (V-Φ) relation of dc superconducting quantum interference devices (SQUIDs) operating at T=77 K is degraded considerably by thermal noise. Since degradation of modulation voltage in the V-Φ relation becomes more significant when inductance increases, a very restricted range of inductance exists which can be used at T=77 K. In order to reduce the degradation due to thermal noise and to enable the use of large inductances, a new SQUID using three Josephson junctions (3J-SQUID) is proposed. Numerical simulation shows that inductance of 3J-SQUID can be increased to twice as large as that of the conventional case without degrading modulation voltage. It is also shown that modulation voltage is highly improved by damping resistance parallel to inductance. As a result, we can expect to use inductances as large as L<500 pH if 3J-SQUID with damping resistance is employed. Large inductances available in 3J-SQUID will be useful in realizing efficient coupling of external magnetic field to the SQUID inductance.

Japanese Journal of Applied Physics•Apr 1, 1994•13 citations

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

Roberto De Luca

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.

ISRN Condensed Matter Physics•Nov 30, 2011•0 citations

Analysis of strong inductive coupling on SQUID systems

Claudia D. Tesche

A technique for the analysis of complex superconducting circuits containing one or more current biased inductively coupled Josephson junction interferometers is described. The equations of motion for the system are shown to separate into a set of non-linear junction equations relating the voltage drops across the junctions to the currents passing through the junctions, and a set of linear equations expressing the quantization of the fluxoid around the superconducting loops and the corresponding linear circuit equations for the normal loops. In many cases, the linear equations can be integrated, resulting in an effective elimination of the normal circuit loops from the problem. The circuit is thus reduced to that of an equivalent set of coupled SQUIDs whose device parameters are a function of the original circuit parameters and the inductive coupling strengths. The dc SQUID tuned linear amplifier is analyzed to display the method. As a result of this analysis, the optimal noise temperature of a tuned SQUID amplifier is derived as a function of the current and voltage noise spectral densities, Svand Sj, and forward transfer function, Vφ. The results obtained demonstrate that the behavior of the SQUID cannot be isolated from that of the rest of the circuit in the manner assumed in previous analyses. The existence of a quantum noise limit on the noise temperature of any phase preserving linear amplifier is used to infer that the noise figures must satisfy the constraint[(S_{v}/2LV_{\phi}^{2})(LS_{j}/2)-S_{vj}^{2}]^{1/2}>\hbarThe behavior of several simple circuits containing a pair of inductively coupled current biased interferometers is discussed to display the extension of the method to circuits containing more than one interferometer.

IEEE Transactions on Magnetics•May 1, 1983•12 citations
Coupling inhomogeneities in the Josephson junctions of planar 0-SQUIDs and π-SQUIDs and of three-dimensional SQUIDs are considered. Starting from the properties of planar SQUIDs, it is shown that slight non-homogeneous couplings of the twelve junctions in three-dimensional superconducting interferometers do not affect the periodicity properties of voltage versus applied flux curves. The results are obtained by applying a rigorous and general analytic approach to planar and three-dimensional superconducting devices.
We present a theoretical study on the dynamical properties of three-dimensional arrays of Josephson junctions. Our results indicate that such superconducting networks represent highly sensitive three-dimensional superconducting quantum interference devices (3D SQUIDs) having some major advantages in comparison with conventional planar SQUIDs. The voltage response function of 3D SQUIDs is directly related to the vector character of external electromagnetic fields. The theory developed here allows the three-dimensional reconstruction of a detected external field including phase information about the field variables. Applications include the design of magnetometers, gradiometers, and particle detectors.
Thin-film Josephson-junction quantum-interference devices require only a small amount of magnetic flux to switch them between the voltage state and the superconducting state. They are sensitive to any spurious magnetic flux present at the device. The magnetic flux may be trapped in the superconducting ground plane, particularly in ground plane holes. This paper analyzes the effects of the trapped magnetic flux on the threshold curves of three-junction Josephson interferometers. The threshold curves of the interferometer are calculated automatically by using a circuit optimization program. The automatic procedure of calculating the threshold curves of an interferometer can be applied to any Josephson-junction interferometer device. The threshold curves of both symmetric and asymmetric interferometers are calculated. We find that the threshold curves of a symmetric three-junction interferometer changes periodically as a function of the effective coupled trapped magnetic flux with a period of Φ0. The threshold curves are shifted and severely distorted in shape by the presence of the coupled trapped magnetic flux. The degeneracy of the threshold curves of a symmetric interferometer makes the unique quantitative determination of the trapped magnetic flux difficult. However, the degeneracy is removed in an asymmetric interferometer. The presence of the unbalanced trapped magnetic flux greatly shifts the entire threshold curve of an asymmetric interferometer.
The dynamic properties of a superconducting quantum interference device (SQUID) containing arrays of Josephson junctions in a superconducting loop, and in particular the case of a four-junction SQUID, is analyzed theoretically via computer simulations. It is shown that phase locking of Josephson junctions determines the dynamic behavior of the SQUID. In the case of a stable phase-lock state hysteretic I-V curves as well as unusual voltage-flux dependencies appear. The influence of a small spread in the Josephson junction parameters upon the stability of the phase-lock state is investigated in parameter space.
It has been shown that the voltage versus flux (V-Φ) relation of dc superconducting quantum interference devices (SQUIDs) operating at T=77 K is degraded considerably by thermal noise. Since degradation of modulation voltage in the V-Φ relation becomes more significant when inductance increases, a very restricted range of inductance exists which can be used at T=77 K. In order to reduce the degradation due to thermal noise and to enable the use of large inductances, a new SQUID using three Josephson junctions (3J-SQUID) is proposed. Numerical simulation shows that inductance of 3J-SQUID can be increased to twice as large as that of the conventional case without degrading modulation voltage. It is also shown that modulation voltage is highly improved by damping resistance parallel to inductance. As a result, we can expect to use inductances as large as L<500 pH if 3J-SQUID with damping resistance is employed. Large inductances available in 3J-SQUID will be useful in realizing efficient coupling of external magnetic field to the SQUID inductance.
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.
A technique for the analysis of complex superconducting circuits containing one or more current biased inductively coupled Josephson junction interferometers is described. The equations of motion for the system are shown to separate into a set of non-linear junction equations relating the voltage drops across the junctions to the currents passing through the junctions, and a set of linear equations expressing the quantization of the fluxoid around the superconducting loops and the corresponding linear circuit equations for the normal loops. In many cases, the linear equations can be integrated, resulting in an effective elimination of the normal circuit loops from the problem. The circuit is thus reduced to that of an equivalent set of coupled SQUIDs whose device parameters are a function of the original circuit parameters and the inductive coupling strengths. The dc SQUID tuned linear amplifier is analyzed to display the method. As a result of this analysis, the optimal noise temperature of a tuned SQUID amplifier is derived as a function of the current and voltage noise spectral densities, Svand Sj, and forward transfer function, Vφ. The results obtained demonstrate that the behavior of the SQUID cannot be isolated from that of the rest of the circuit in the manner assumed in previous analyses. The existence of a quantum noise limit on the noise temperature of any phase preserving linear amplifier is used to infer that the noise figures must satisfy the constraint[(S_{v}/2LV_{\phi}^{2})(LS_{j}/2)-S_{vj}^{2}]^{1/2}>\hbarThe behavior of several simple circuits containing a pair of inductively coupled current biased interferometers is discussed to display the extension of the method to circuits containing more than one interferometer.