Distribution of flux states in a hysteretic dc SQUID

Abstract This work investigates the distribution of flux states of hysteretic dc superconducting quantum interference devices (SQUIDs) obtained from standard current ramp measurement at 2.50 and 0.35 K. Each flux state corresponds to a specific number of flux quanta trapped in the superconducting loop, associated with a metastable state in the two-dimensional potential energy of the hysteretic SQUID. The flux states can be distinguished by the multiple switching currents. The observed distribution is different from the distribution caused only by thermal excitation at a specific temperature. There are notable systematic deviations between the measurement results of three samples and the standard Boltzmann distribution, which can be clearly identified from the ratios between the proportions of different flux states. A formula resembling the Boltzmann distribution, involving multiple effective temperatures, is proposed to provide a better fit to the measured results. The finding suggests that the observed distribution of flux states is established during the SQUID’s transition from the dissipative state to the zero-voltage state, and multiple equivalent temperatures may be involved in the process.