Constriction-based Josephson weak links display a thermal bistability between two states exhibiting zero and finite voltages. This manifests in experiments either as hysteresis in the current-voltage characteristics of weak links or as a random telegraphic signal in voltage. In the latter case, a noise-driven amplification of a sinusoidal excitation of the device is observed, at frequencies matching the characteristic switching frequency in the telegraphic signal, a phenomenon known as stochastic resonance. The observed behavior is understood using a two-state model of stochastic resonance and is exploited to illustrate an enhanced signal-to-noise-ratio in a μ-SQUID as a magnetic field sensor.

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