A thermal activation model is described for the dc SQUID. The equations of motion for the junction phase differences are shown to develop in time like the coordinates of a particle performing Brownian motion in a viscous medium in a two-dimensional potential field. Expressions are derived relating the average voltage, transfer function, and current and voltage noise spectral densities to the features of the potential determined by the device parameters. Comparison with a numerical simulation is presented. Calculations of the current noise as a function of loop inductance and critical current asymmetry are performed. An anomalously large current noise is predicted at certain values of the device characteristics. The correlation spectral density is also calculated as a function of loop inductance, and related to the optimal source resistance for a tuned SQUID amplifier. A theory of low-frequency noise sources in the SQUID is developed in a fashion compatible with the thermal activation model. Equilibrium temperature fluctuations as a possible source of 1/f noise in the SQUID are discussed. A scheme for optimizing the resolution at low frequencies is presented. Proper exploitation of low-capacitance Pb-PbOx-Pb junction technology is shown to increase the resolution at 1 Hz by at least a factor of 8, provided that the temperature fluctuations are the dominant source of noise.
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Work supported in part by ONR under contract #NR319-154.
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Tesche, C.D. A thermal activation model for noise in the dc SQUID. J Low Temp Phys 44, 119–147 (1981). https://doi.org/10.1007/BF00115079
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DOI: https://doi.org/10.1007/BF00115079