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Bulletin of the American Physical Society

Johnson noise measurements of a 3.1 k$\Omega$ resistor at mK temperatures using a SQUID-based circuit

Vidhi Shingla, Ethan Kleinbaum, G 'abor Cs 'athy

Published Mar 15, 2017• 0 citations
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Johnson noise measurements of a 3.1 kΩ\OmegaΩ resistor at mK temperatures using a SQUID-based circuit
We present a dc Superconducting QUantum Interference Device (SQUID)-based current amplifier with an estimated input referred noise of only 2.3 fA/Hz. Because of such a low amplifier noise, the circuit is useful for Johnson noise thermometry of quantum resistors in the kΩ range down to mK temperatures. In particular, we demonstrate that our circuit does not contribute appreciable noise to the Johnson noise of a 3.25 kΩ resistor down to 16 mK. Our circuit is a useful alternative to the commonly used High Electron Mobility Transistor-based amplifiers, but in contrast to the latter, it offers a much reduced 1/f noise. In comparison to SQUIDs interfaced with cryogenic current comparators, our circuit has similar low noise levels, but it is easier to build and to shield from magnetic pickup.
The impedance and noise of a resistive superconductive quantum interference device (R-SQUID) have been measured as a function of the dc and rf currents applied to it. The Josephson junction was adjustable so that data were also taken for several values of the junction critical current. The results were compared with the predictions of a resistively shunted junction (RSJ) model which takes into account the influence of the Josephson junction on the impedance and noise. The agreement was found to be quite good and demonstrates that the noise in the circuit is well understood. Use of the R-SQUID as a noise thermometer below 1 K is assessed in terms of corrections due to the RSJ model. It is demonstrated how the dc and rf currents may be adjusted so that the total noise of the R-SQUID is reduced to within 0.1% of the Johnson noise generated by the resistor alone. Under these conditions, the R-SQUID may be used as a noise thermometer to determine thermodynamic temperature to this inaccuracy from 6 to 700 mK.
The generally accepted noise theory of the dc SQUID predicts that the energy resolution scales as the electron temperature in the Josephson junction shunt resistors. As in metals at low temperature the electron-phonon coupling becomes very weak, the electron gas of the thin film shunt resistors undergoes a Joule heating due to the bias current and its temperature can be significantly higher than that of the thermal bath. This heating, the hot-electron effect, causes a deviation from the linear behaviour of noise versus temperature and a saturation of the SQUID noise, typically at temperatures of about 200 mK. This effect can be reduced considerably by increasing the effective volume available for the electron-phonon interaction by attaching "large" cooling fins to the shunt resistors. Our measurements have been performed on two thin film devices made with the same design of a dc SQUID but without the Josephson junctions: one device with standard shunt resistors, the other with shunt resistors with cooling fins. From these measurements one can expect for the SQUID with cooling fins an improvement of the noise saturation temperature of at most a factor 2, from 200 mK to about 100 mK.