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APPROACH TO THE QUANTUM NOISE LIMIT IN THE DC SQUID

Dale J. Van Harlingen, R. H. Koch, Jim A. Clarke

Published Nov 1, 1981• 0 citations
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Abstract

Tunnel junction dc SQUIDs designed to approach the quantum noise limit in the temperature range. 1 to 4K were fabricated with an inductance of about 2 pH and a capacitance per junction of about 0.5 pF.The lowest.measured noise energy was 3.2h at 1.4K at a frequency of 202kHz.When the 1/f noise was subtracted, the white noise energy decreased from around 3b at 4.2K to below 2h at 1.4K.. .

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Tunnel junction dc SQUIDs designed to approach the quantum noise limit in the temperature range. 1 to 4K were fabricated with an inductance of about 2 pH and a capacitance per junction of about 0.5 pF.The lowest.measured noise energy was 3.2h at 1.4K at a frequency of 202kHz.When the 1/f noise was subtracted, the white noise energy decreased from around 3b at 4.2K to below 2h at 1.4K.. .
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 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 have fabricated and characterized the noise performance of submicron edge junction dc superconducting quantum interference devices (SQUID’s) which exhibit excellent signal properties and extremely high flux sensitivity. At frequencies above about 3 MHz, the SQUID noise is white and is in reasonable agreement with computer simulations for a thermal noise-limited detector. In one device the measured flux energy resolution is 1.6±0.5ℏ at 1.5 K, within a factor of 2 of the quantum-limited value suggested by theoretical modeling.
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.
We present the results of an investigation of thin-film dc super conducting quantum interference device (SQUID’s) with very high energy resolution. The SQUID’s were fabricated using integrated-circuit techniques appropriate for superconducting devices. A weakly coupled SQUID with very low inductance (1 pH) had an intrinsic energy sensitivity 6×10−34 J/Hz = 0.9 h. A well-coupled SQUID (coupling constant α = 0.43) had an energy sensitivity referred to the input coil of 4.7×10−32 J/Hz = 71 h.