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 K 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. It shows good agreement with a quasi-Boltzmann distribution with multiple different inverse temperatures, dependent on the bottom energy of the potential wells and featuring a short equilibrium time. The standard Boltzmann distribution is insufficient to accurately describe the observed 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.
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