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

Journal of Applied Physics

Superconducting single-junction interferometers with small critical currents

Paul K. Hansma

Published Sep 1, 1973• 56 citations
Publisher

Abstract

A simple theory of the superconducting single-junction interferometer (ac Squid) becomes possible if the critical current of the single junction is small relative to Φ0/LR, where Φ0=h/2e is one flux quantum and LR is the inductance of the interferometer loop. This theory predicts a magnetic flux sensitivity which has the same dependence on interferometer parameters as the existing theories for higher critical currents. In contrast to those theories, however, the present theory predicts that the maximum flux sensitivity will be achieved off resonance. Theoretical predictions for comparison with experiment are displayed as a function of the normalized difference between the operating frequency ω and the resonant frequency ω0.

DOI
10.1063/1.1662916

Related papers

Limiting characteristics of a superconducting quantum interferometer. I. Signal characteristic

Eugene I. Butikov, S.P. Feofilov

The operation of a constant-current quantum interferometer with two Josephson junctions is studied in a system for measuring small changes in a magnetic field with low-frequency modulation of the magnetic flux. Idealized theoretical signal characteristics are found together with their dependence on the operating mode and parameters of a SQUID. These characteristics are used in Pt. II (ref. 12) to determine the minimal detectable change in the magnetic flux, which characterizes the maximal sensitivity of a SQUID.

•Nov 1, 1980•0 citations

Effect of nonequilibrium phenomena in a superconducting point contact on the properties of a single-contact quantum interferometer

V. A. Khlus

The behavior of a superconducting ring incorporating a point contact, coupled inductively to an oscillatory circuit (hf SQUID), with the rate of change of the magnetic flux in the ring being comparable, to the inverse energy relaxation time of excitations in the superconductor τϵ−1, is examined. For T ∽ Tc the results of the microscopic theory of the nonstationary behavior of point contacts, in which the coupling between the phase difference and the current of the Josephson junction differs from the usual expression I = V/R + Icsinφ in the resistive model, are used. It is shown that the nonequilibrium behavior of a weak link for ω≳τϵ−1 significantly changes the amplitude–frequency and signal characteristics of the SQUID as compared with the case ωτϵ−1≪1, for which the results based on the resistive model are valid. The characteristics of the SQUID in the nonequilibrium situation are sensitive to the ratio between the size of the contact and the mean free path of electrons relative to scattering by impurities.

Soviet Journal of Low Temperature Physics•Jan 1, 1984•0 citations

An ultra-low-noise tunnel junction dc SQUID

M. B. Ketchen, Richard F. Voss

The design, fabrication, and noise properties of an ultra-low-noise tunnel junction dc SQUID (superconducting quantum interference device) are presented. The two resistively shunted Pb-alloy tunnel junctions are each 3.6 μm diam. The SQUID has an inductance L of ≈11 pH, a critical current per junction, I0 of ≈100 μA, and a resistance per shunt R of ≈2 Ω. At 2.3 K, eI0R≈kBT, and simple theory predicts that the minimum intrinsic energy sensitivity should be ≈2h. The actual minimum value of the measured high-frequency (70 kHz) flux noise at 4.2 K is φn=1.3×10−7φ0 Hz−1/2. This corresponds to an intrinsic energy sensitivity, φ2n/2L, of 3.2×10−33 J Hz−1 or 5h. Lowering the bath temperature to 1.8 K gave no improvement in performance.

Applied Physics Letters•Nov 15, 1979•61 citations

Suppression of the critical current of a balanced superconducting quantum interference device

A. Kemppinen, Antti J. Manninen, Mikko Möttönen +3 more

We present an experimental study of the magnetic flux dependence of the critical current of a balanced superconducting quantum interference device (SQUID) with three Josephson junctions in parallel. Unlike for ordinary direct current (dc) SQUIDs, the suppression of the critical current does not depend on the exact parameters of the Josephson junctions. The suppression is essentially limited only by the inductances of the SQUID loops. We demonstrate a critical current suppression ratio of higher than 300 in a balanced SQUID with a maximum critical current 30nA.

arXiv:0712.0063•Applied Physics Letters•Feb 4, 2008•15 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

Properties of the microwave SQUID with an YBaCuO point contact junction

Tapani Ryhänen, Heikki Seppä

A high-sensitivity microwave SQUID (superconducting quantum interference device), suitable for RF attenuation measurements, is constructed taking advantage of the low density of states of current carriers in high-T/sub c/ materials. The dynamics, the noise properties, and the sensitivity of the microwave SQUID are theoretically analyzed. The ultimate energy resolution of the waveguide SQUID is inversely proportional to the characteristic frequency omega /sub c/=R/sub q//L of the loop. omega /sub c/ is high for YBaCuO junctions at 4.2 K because of small leakage. A flux sensitivity of 4*10/sup 4-6/ phi /sub 0// square root Hz has been achieved, which is in good agreement with the theoretical predictions.>

IEEE Transactions on Magnetics•Mar 1, 1989•2 citations
A simple theory of the superconducting single-junction interferometer (ac Squid) becomes possible if the critical current of the single junction is small relative to Φ0/LR, where Φ0=h/2e is one flux quantum and LR is the inductance of the interferometer loop. This theory predicts a magnetic flux sensitivity which has the same dependence on interferometer parameters as the existing theories for higher critical currents. In contrast to those theories, however, the present theory predicts that the maximum flux sensitivity will be achieved off resonance. Theoretical predictions for comparison with experiment are displayed as a function of the normalized difference between the operating frequency ω and the resonant frequency ω0.
The operation of a constant-current quantum interferometer with two Josephson junctions is studied in a system for measuring small changes in a magnetic field with low-frequency modulation of the magnetic flux. Idealized theoretical signal characteristics are found together with their dependence on the operating mode and parameters of a SQUID. These characteristics are used in Pt. II (ref. 12) to determine the minimal detectable change in the magnetic flux, which characterizes the maximal sensitivity of a SQUID.
The behavior of a superconducting ring incorporating a point contact, coupled inductively to an oscillatory circuit (hf SQUID), with the rate of change of the magnetic flux in the ring being comparable, to the inverse energy relaxation time of excitations in the superconductor τϵ−1, is examined. For T ∽ Tc the results of the microscopic theory of the nonstationary behavior of point contacts, in which the coupling between the phase difference and the current of the Josephson junction differs from the usual expression I = V/R + Icsinφ in the resistive model, are used. It is shown that the nonequilibrium behavior of a weak link for ω≳τϵ−1 significantly changes the amplitude–frequency and signal characteristics of the SQUID as compared with the case ωτϵ−1≪1, for which the results based on the resistive model are valid. The characteristics of the SQUID in the nonequilibrium situation are sensitive to the ratio between the size of the contact and the mean free path of electrons relative to scattering by impurities.
The design, fabrication, and noise properties of an ultra-low-noise tunnel junction dc SQUID (superconducting quantum interference device) are presented. The two resistively shunted Pb-alloy tunnel junctions are each 3.6 μm diam. The SQUID has an inductance L of ≈11 pH, a critical current per junction, I0 of ≈100 μA, and a resistance per shunt R of ≈2 Ω. At 2.3 K, eI0R≈kBT, and simple theory predicts that the minimum intrinsic energy sensitivity should be ≈2h. The actual minimum value of the measured high-frequency (70 kHz) flux noise at 4.2 K is φn=1.3×10−7φ0 Hz−1/2. This corresponds to an intrinsic energy sensitivity, φ2n/2L, of 3.2×10−33 J Hz−1 or 5h. Lowering the bath temperature to 1.8 K gave no improvement in performance.
We present an experimental study of the magnetic flux dependence of the critical current of a balanced superconducting quantum interference device (SQUID) with three Josephson junctions in parallel. Unlike for ordinary direct current (dc) SQUIDs, the suppression of the critical current does not depend on the exact parameters of the Josephson junctions. The suppression is essentially limited only by the inductances of the SQUID loops. We demonstrate a critical current suppression ratio of higher than 300 in a balanced SQUID with a maximum critical current 30nA.
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.
A high-sensitivity microwave SQUID (superconducting quantum interference device), suitable for RF attenuation measurements, is constructed taking advantage of the low density of states of current carriers in high-T/sub c/ materials. The dynamics, the noise properties, and the sensitivity of the microwave SQUID are theoretically analyzed. The ultimate energy resolution of the waveguide SQUID is inversely proportional to the characteristic frequency omega /sub c/=R/sub q//L of the loop. omega /sub c/ is high for YBaCuO junctions at 4.2 K because of small leakage. A flux sensitivity of 4*10/sup 4-6/ phi /sub 0// square root Hz has been achieved, which is in good agreement with the theoretical predictions.>