Abstract

The Josephson junction can be used to convert voltage into frequency and thus it can be used to convert voltage fluctuations generated by Johnson noise in a resistor into frequency fluctuations. As a consequence, the temperature of the resistor can be defined by measuring the variance of the frequency fluctuations. Unfortunately, the absolute determination of temperature by this approach is disturbed by several undesirable effects: a rolloff introduced by the bandwidth of the postdetection filter, additional noise caused by rf amplifiers, and a mixed noise effect caused by the nonlinearity of the Josephson junction together with rf noise in the tank circuit. Furthermore, the variance is a statistical quantity and therefore the limited number of frequency counts produces inaccuracy in a temperature measurement. In this work the total inaccuracy of the noise thermometer is analyzed and the optimal choice of the parameters is derived. A practical way to find the optimal conditions for the Josephson junction noise thermometer is discussed. The inspection shows that under the optimal conditions the total error is dependent only on the temperature under determination, the equivalent noise temperature of the preamplifier, the bias frequency of the SQUID, and the total time used for the measurement.

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