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

Thermal noise-limited sensitivity of the pulse-biased SQUID magnetometer

Norio Fujimaki, Hirotaka Tamura, Takeshi Imamura, S. Hasuo

Published Feb 15, 1989• 9 citations
Publisher

Abstract

We numerically calculated and obtained an approximate expression for the thermal noise-limited sensitivity of the pulse-biased SQUID sensor used in the integrated magnetometer. We found that the sensitivity is inversely proportional to the bias frequency and inversely proportional to the critical current of the Josephson junction to the 4/3 power. The sensitivity is also proportional to the temperature to the 4/3 power, and is nearly independent of the bias pulse duration. The sensitivity expression is similar to that of the rf SQUID, however, the coefficient is more than one order of magnitude smaller. The best sensitivity has the same order of magnitude as that of the dc SQUID. The quantum limit is attained at a bias frequency of 0.9 GHz at 4.2 K with the typical junction parameters. This sensitivity is available for the SQUID magnetometer operated in the digital feedback loop.

DOI
10.1063/1.342955

Related papers

Limit characteristics of two-junction magnetic flux detector

Victor I. Danilov, K. K. Likharev, O. Sniguiriev +1 more

The sensitivity of a two-Josephson-junction interferometer as a magnetic flux detector (dc SQUID) is estimated. The minimum value of the basic SQUID characteristic-noise equivalent temperature δT = (δΦ)2/kBL appears to be as low as for the best rf SQUID mode:(\deltaT)_{\min}/(\Deltaf)\cong 3 T/f_{o}. HereTis an operating temperature, fois a characteristic frequency of the Josephson junctions and\Deltafis a post-detector bandwidth. For a typical value of SQUID inductance L this limit corresponds to flux sensitivity of the order of 10-7Φo/Hz1/2.

IEEE Transactions on Magnetics•Jan 1, 1977•8 citations

Thermal-noise-limited performance in single-chip superconducting quantum interference devices

Norio Fujimaki, K. Gotoh, T. Imamura +1 more

The single-chip superconducting quantum interference device (SQUID) we made using niobium Josephson junctions integrates a two-junction SQUID and a superconducting feedback circuit. The switching probability, its derivative to input flux, and the flux spectral density measured by varying the sinusoidal bias frequency and amplitude agree well with thermal noise theory. The best sensitivity and cutoff frequency were 6.2×10−6 Φ0■√Hz and 1.1 kHz for a bias frequency at 10 MHz. The dynamic range was 2.5×105. These data show the SQUID to be suited to practical biomagnetic application.

Journal of Applied Physics•Jun 15, 1992•9 citations

Temperature-dependent performance of all-NbN DC-SQUID magnetometers

Quansheng Liu, Huiwu Wang, Qiyu Zhang +3 more

Integrated NbN direct current superconducting quantum interference device (DC-SQUID) magnetometers were developed based on high-quality epitaxial NbN/AlN/NbN Josephson junctions for SQUID applications operating at high temperatures. We report the current–voltage and voltage–flux characteristics and the noise performance of the NbN DC-SQUIDs for temperatures ranging from 4.2 to 9 K. The critical current and voltage swing of the DC-SQUIDs decreased by 15% and 25%, respectively, as the temperature was increased from 4.2 to 9 K. The white flux noise of the DC-SQUID magnetometer at 1 kHz increased from 3.9 μΦ0/Hz1/2 at 4.2 K to 4.8 μΦ0/Hz1/2 at 9 K with 23% increase, corresponding to the magnetic field noise of 6.6 and 8.1 fT/Hz1/2, respectively. The results show that NbN DC-SQUIDs improve the tolerance of the operating temperatures and temperature fluctuations in SQUID applications.

Applied Physics Letters•May 29, 2017•17 citations

Advances in SQUID magnetometers

John L. Clarke

The operation and noise limitations of de and RF SQUID's are outlined, and recent advances in their sensitivity are discussed. A model of the dc SQUID predicts an energy noise level per hertz referred to the SQUID of approximately8 k_{B}TL/R \approx 8 k_{B}T(\piLC)^{1/2}, whereL, R,andCare the SQUID inductance and the shunt resistance and capacitance of each Josephson junction. Some examples of dc SQUID's are described to show that their performance is generally in reasonable agreement with the model. The noise energy has improved from about 2 × 10-30J. Hz-1for a device withL = 1nH and a tunnel junction area of 104µm2to about 2 × 10-33J . Hz-1for a device withL = 0.1nH and a microbridge resistance of 40 Ω. Further improvements axe expected in the near future. The model of the RF SQUID predicts a noise energy per hertz referred to the SQUID of[(\pi\alpha^{2}\phi\min{0}\max{2}/2L) + 2 \pi \alpha k_{B}T\min{a}\max{(eff)}]/\omega_{RF}, where α is the intrinsic width of the distribution of flux transitions,T\min{a}\max{(eff)}is an effective amplifier noise temperature, and ωRFis the pump frequency. With one exception, the performance of the seven types of RF SQUID listed is in reasonable agreement with the model. The noise energy ranges from about 1.5 × 10-29J . Hz-1for a 20-MHz toroidal SQUID to 3.5 × 10-31J . Hz-1for 9-GHz reentrant toroidal SQUID; a somewhat better sensitivity has been reported for a 430-MHz device, apparently in conflict with the theory. In both dc and RF SQUID's, 1/fnoise (fis frequency) is likely to extend to higher frequencies as the white-noise level is decreased.

IEEE Transactions on Electron Devices•Oct 1, 1980•88 citations

The dc SQUID near the quantum noise limit

D. J. VanHarlingen, R. H. Koch, Jim A. Clarke

A series of dc SQUIDs has been fabricated in an attempt to obtain quantum-limited sensitivity. Typically, the SQUID inductance, L, is 2 pH, the capacitance and critical current of each tunnel junction are 0.5 pF and 0.5 mA, and the shunt resistance for each junction is 1Ω. The measured spectral density of the voltage noise Sv contains a l/f component that extends typically to 100 kHz or higher. When the l/f component is subtracted out, the best energy sensitivity achieved to date is ε1Hz = Sv2L(θVθΦ)2 less than or approximately equal to 2h, where θV/θΦ PHI is the transfer coefficient.

•Jan 1, 1981•0 citations

Quantum noise in SQUIDs

Вадим Васильевич Данилов, K. K. Likharev, Alexander B Zorin

The sensitivity limitations due to thermal, quantum and shot noise are calculated for dc and ac SQUIDs. Two approximations are used for the Josephson junctions: i. RSJ model with the equilibrium source of thermal-and-quantum fluctuations and ii. microscopic theory of the tunnel junctions with small capacitance (the latter theory takes into account the shot noise as well). The ultimate "output" sensitivity ε_{V}=/2L\Deltaf is shown to be substantially less than the Planck's constant h, for the both types of SQUIDs. This result does not contradict to the uncertainty principle, because the "total" sensitivity ε=(ε_{V}ε_{I}-εmin{IV}\max{2})^{1/2} rather than ε_{V} is an adequate figure of merit of SQUID as a linear amplifier. The total sensitivity is shown to be, in fact, limited by the quantum fluctuations, ε>h/2. These fluctuations originate in the shunting resistances of the dc SQUID, while in the ac SQUID they are due to quantum noise of the following stage of amplification. Nevertheless, even the total sensitivity ε can be made less than h/2, if the "degenerate" type of SQUID is used, being sensitive to the only one of the quadrature components of the input signal.

IEEE Transactions on Magnetics•May 1, 1983•47 citations
We numerically calculated and obtained an approximate expression for the thermal noise-limited sensitivity of the pulse-biased SQUID sensor used in the integrated magnetometer. We found that the sensitivity is inversely proportional to the bias frequency and inversely proportional to the critical current of the Josephson junction to the 4/3 power. The sensitivity is also proportional to the temperature to the 4/3 power, and is nearly independent of the bias pulse duration. The sensitivity expression is similar to that of the rf SQUID, however, the coefficient is more than one order of magnitude smaller. The best sensitivity has the same order of magnitude as that of the dc SQUID. The quantum limit is attained at a bias frequency of 0.9 GHz at 4.2 K with the typical junction parameters. This sensitivity is available for the SQUID magnetometer operated in the digital feedback loop.
The sensitivity of a two-Josephson-junction interferometer as a magnetic flux detector (dc SQUID) is estimated. The minimum value of the basic SQUID characteristic-noise equivalent temperature δT = (δΦ)2/kBL appears to be as low as for the best rf SQUID mode:(\deltaT)_{\min}/(\Deltaf)\cong 3 T/f_{o}. HereTis an operating temperature, fois a characteristic frequency of the Josephson junctions and\Deltafis a post-detector bandwidth. For a typical value of SQUID inductance L this limit corresponds to flux sensitivity of the order of 10-7Φo/Hz1/2.
The single-chip superconducting quantum interference device (SQUID) we made using niobium Josephson junctions integrates a two-junction SQUID and a superconducting feedback circuit. The switching probability, its derivative to input flux, and the flux spectral density measured by varying the sinusoidal bias frequency and amplitude agree well with thermal noise theory. The best sensitivity and cutoff frequency were 6.2×10−6 Φ0■√Hz and 1.1 kHz for a bias frequency at 10 MHz. The dynamic range was 2.5×105. These data show the SQUID to be suited to practical biomagnetic application.
Integrated NbN direct current superconducting quantum interference device (DC-SQUID) magnetometers were developed based on high-quality epitaxial NbN/AlN/NbN Josephson junctions for SQUID applications operating at high temperatures. We report the current–voltage and voltage–flux characteristics and the noise performance of the NbN DC-SQUIDs for temperatures ranging from 4.2 to 9 K. The critical current and voltage swing of the DC-SQUIDs decreased by 15% and 25%, respectively, as the temperature was increased from 4.2 to 9 K. The white flux noise of the DC-SQUID magnetometer at 1 kHz increased from 3.9 μΦ0/Hz1/2 at 4.2 K to 4.8 μΦ0/Hz1/2 at 9 K with 23% increase, corresponding to the magnetic field noise of 6.6 and 8.1 fT/Hz1/2, respectively. The results show that NbN DC-SQUIDs improve the tolerance of the operating temperatures and temperature fluctuations in SQUID applications.
The operation and noise limitations of de and RF SQUID's are outlined, and recent advances in their sensitivity are discussed. A model of the dc SQUID predicts an energy noise level per hertz referred to the SQUID of approximately8 k_{B}TL/R \approx 8 k_{B}T(\piLC)^{1/2}, whereL, R,andCare the SQUID inductance and the shunt resistance and capacitance of each Josephson junction. Some examples of dc SQUID's are described to show that their performance is generally in reasonable agreement with the model. The noise energy has improved from about 2 × 10-30J. Hz-1for a device withL = 1nH and a tunnel junction area of 104µm2to about 2 × 10-33J . Hz-1for a device withL = 0.1nH and a microbridge resistance of 40 Ω. Further improvements axe expected in the near future. The model of the RF SQUID predicts a noise energy per hertz referred to the SQUID of[(\pi\alpha^{2}\phi\min{0}\max{2}/2L) + 2 \pi \alpha k_{B}T\min{a}\max{(eff)}]/\omega_{RF}, where α is the intrinsic width of the distribution of flux transitions,T\min{a}\max{(eff)}is an effective amplifier noise temperature, and ωRFis the pump frequency. With one exception, the performance of the seven types of RF SQUID listed is in reasonable agreement with the model. The noise energy ranges from about 1.5 × 10-29J . Hz-1for a 20-MHz toroidal SQUID to 3.5 × 10-31J . Hz-1for 9-GHz reentrant toroidal SQUID; a somewhat better sensitivity has been reported for a 430-MHz device, apparently in conflict with the theory. In both dc and RF SQUID's, 1/fnoise (fis frequency) is likely to extend to higher frequencies as the white-noise level is decreased.
A series of dc SQUIDs has been fabricated in an attempt to obtain quantum-limited sensitivity. Typically, the SQUID inductance, L, is 2 pH, the capacitance and critical current of each tunnel junction are 0.5 pF and 0.5 mA, and the shunt resistance for each junction is 1Ω. The measured spectral density of the voltage noise Sv contains a l/f component that extends typically to 100 kHz or higher. When the l/f component is subtracted out, the best energy sensitivity achieved to date is ε1Hz = Sv2L(θVθΦ)2 less than or approximately equal to 2h, where θV/θΦ PHI is the transfer coefficient.
The sensitivity limitations due to thermal, quantum and shot noise are calculated for dc and ac SQUIDs. Two approximations are used for the Josephson junctions: i. RSJ model with the equilibrium source of thermal-and-quantum fluctuations and ii. microscopic theory of the tunnel junctions with small capacitance (the latter theory takes into account the shot noise as well). The ultimate "output" sensitivity ε_{V}=/2L\Deltaf is shown to be substantially less than the Planck's constant h, for the both types of SQUIDs. This result does not contradict to the uncertainty principle, because the "total" sensitivity ε=(ε_{V}ε_{I}-εmin{IV}\max{2})^{1/2} rather than ε_{V} is an adequate figure of merit of SQUID as a linear amplifier. The total sensitivity is shown to be, in fact, limited by the quantum fluctuations, ε>h/2. These fluctuations originate in the shunting resistances of the dc SQUID, while in the ac SQUID they are due to quantum noise of the following stage of amplification. Nevertheless, even the total sensitivity ε can be made less than h/2, if the "degenerate" type of SQUID is used, being sensitive to the only one of the quadrature components of the input signal.