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Applied Physics Letters

Back action of a low noise dc SQUID

P. Falferi, M. Bonaldi, MASSIMO CERDONIO, Andrea Vinante, Stefano Vitale

Published Dec 14, 1998• 14 citations
Publisher

Abstract

Measurements are presented of the back action of a low noise commercial dc superconducting quantum interference device (SQUID) on a strongly-coupled high-quality factor (Q≈106) electrical LC resonator operating at audio frequencies (≈1 kHz). The back-action effect, due to the voltage noise of the SQUID current amplifier, is in good agreement with the predictions. The value of the noise impedance of the SQUID coincides, within 5%, with its input coil inductance times the angular frequency.

DOI
10.1063/1.122833

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Input impedance of an amplifier based on a dc superconducting quantum interference device

Claude Hilbert, John L. Clarke

The measured input impedance of an amplifier involving a coil tightly coupled to a dc superconducting quantum interference device (SQUID) is found to depend on the current and flux biases of the SQUID. Variations in the input inductance arise from the reflected dynamic inductance of the SQUID, and are in reasonable agreement with the predictions of an analog simulator. Variations in the input resistance, on the other hand, arise from feedback between the output of the SQUID and the input circuit, and are in approximate agreement with the predictions of a simple model.

Applied Physics Letters•Oct 1, 1984•15 citations
Measurements are presented of the back action of a low noise commercial dc superconducting quantum interference device (SQUID) on a strongly-coupled high-quality factor (Q≈106) electrical LC resonator operating at audio frequencies (≈1 kHz). The back-action effect, due to the voltage noise of the SQUID current amplifier, is in good agreement with the predictions. The value of the noise impedance of the SQUID coincides, within 5%, with its input coil inductance times the angular frequency.
The coupling effects of a commercial dc superconducting quantum interference device (SQUID) to an electrical LC resonator which operates at audio frequencies (≈1 kHz) with quality factors Q≈106 are presented. The variations of the resonance frequency of the resonator as functions of the flux applied to the SQUID are due to the SQUID dynamic inductance in good agreement with the predictions of a model. The variations of the quality factor point to a feedback mechanism between the output of the SQUID and the input circuit.
A two-stage superconducting quantum interference device (SQUID), based on a commercial sensor, is strongly coupled to an electrical resonator at 11 kHz with a quality factor Q=600 000 and operated in the temperature range 1.33–4.17 K. From the analysis of the noise generated by this system, the back action noise of the SQUID amplifier is estimated. The minimum noise temperature, calculated from back action and additive noise measurements, is 63 μK at 1.33 K, and corresponds to 120 times the quantum-limited noise temperature. We discuss and experimentally verify a mechanism, which can limit the noise temperature and add losses to the system.
A low-noise coupled DC superconducting quantum interference device (SQUID) especially optimized for low frequency is discussed. Using large Josephson junctions and a low loop inductance the contribution of the critical current fluctuation to 1/f noise can be minimized. To minimize the inductance the Josephson junctions are placed in the center of the washer close to the SQUID loop. A scaled-up copper model of the SQUID and the signal coil is used to analyze the impedance of the SQUID loop affected by the signal coil. An equivalent circuit model describing the effective inductance of the SQUID loop as a function of the frequency is used to design appropriate damping of the resonances. The DC SQUID characteristics are smooth and the noise performance of the SQUID does not markedly suffer from resonances. The contribution of the 1/f noise at 1 Hz is found to be about 5*10/sup -7/ Phi /sub 0// square root Hz.>
The dynamics and noise of a dc SQUID (the Superconducting Quantum Interference Device), with the McCumber parameter /spl beta//sub c/=2/spl pi/R/sup 2/l/sub c/C//spl Phi//sub 0/ close to the unity (where I/sub c/, R, C is the critical current, the shunt resistance and the capacitance of the Josephson junctions comprising the SQUID, respectively, /spl Phi//sub 0/=2.07 10/sup -15/ Wb is the magnetic flux quantum) integrated with a planar spiral input coil, have been experimentally studied. The length of the spiral input coil was chosen so as to match its /spl lambda//4 microwave resonance frequency to the plasma resonance frequency of the SQUID. The input coil resonance is found to enhance the overall quality factor Q of the Josephson oscillations in the SQUID and, as a result, to increase the dynamic resistance R/sub d/ and the gradient of the flux-to-voltage characteristics, /spl delta/V//spl delta//spl Phi/, without hysteresis. A dc SQUID with a loop inductance L=30.5 pH, /spl beta//sub c/=0.72, and a 6 turn input coil demonstrated a non-distorted quasi-sinusoidal flux-to-voltage transfer function with an exceptionally large modulation depth of 140 /spl mu/V peak-to-peak. The spectral density of the magnetic flux noise was as low as 3.5/spl times/10/sup -7/ /spl Phi//sub 0//Hz/sup 1/2/ in the double stage configuration, measured at a temperature 4.2 K using direct read out electronics. In combination with an intermediary transformer, the current resolution of the SQUID is as low as 1.25 pA/Hz/sup 1/2/ with an input coil inductance of 100 nH.
The dc Superconducting Quantum Interference Device (dc-SQUID) is one of the most sensitive magnetic field sensors available. In this thesis we concentrate on its application as an amplifier. In this configuration, an input circuit of interest can be connected by means of a coupling coil. The intended application of our developed low-Tc SQUID amplifiers is the readout of the first spherical gravitational wave antenna MiniGRAIL. Using small-signal analysis as well as numerical simulations, we study the achievable signal-to-noise ratio of such sensors in practical measurements. Published theories and studies could be extended. Some interesting points treated are the influence of the often used negative feedback (flux-locked loop), an altered input impedance of the SQUID amplifier and the influence of back-action noise, which directly affects the object of interest. The altered operation of the SQUID due to the presence of the input circuit is studied in numerical experiments. Another important issue, the influence of integrated input coils on the dynamics of SQUIDs, is investigated theoretically and experimentally. The performance of our developed sensors is compared to numerical simulations on detailed models. The results give insights into the behavior, design and usage of dc-SQUIDs with integrated coils. For a SQUID with input inductances of 1.5 μH we reached a good coupled energy sensitivity of about 170 ¯h in a dilution refrigerator. Furthermore, we investigated the hot-electron effect. This effect typically limits the sensitivity of superconducting electronics at sub-Kelvin bath temperatures due to a weakened electron-phonon coupling. We performed heating experiments on thin-film resistors which are similar to the shunt resistors of the Josephson junctions used in our sensors. The suppression of the hot-electron effect via electronic thermal transport to attached cooling fins is investigated both experimentally, theoretically and numerically. The numerical technique turns out to be a useful tool for the thermal design of superconducting electronics.
The measured input impedance of an amplifier involving a coil tightly coupled to a dc superconducting quantum interference device (SQUID) is found to depend on the current and flux biases of the SQUID. Variations in the input inductance arise from the reflected dynamic inductance of the SQUID, and are in reasonable agreement with the predictions of an analog simulator. Variations in the input resistance, on the other hand, arise from feedback between the output of the SQUID and the input circuit, and are in approximate agreement with the predictions of a simple model.