  Superconducting weak link (WL), acting as a Josephson junction (JJ), is one
of the widely used elements in superconductor science and quantum circuits. A
hysteretic JJ with robust switching between its superconducting and resistive
state is an excellent candidate for single-photon detection. However, the
ubiquitous fluctuations in the junction strongly influence the stability of the
states and, thus, the transition from one to the other. Here, we present an
experimental study of switching statistics of critical and retrapping currents
of a JJ based on niobium WL in its hysteretic regime. The mean lifetimes of the
two metastable states, namely, the zero-voltage superconducting state and
finite-voltage resistive state, are estimated from the distributions. Further,
close to the hysteresis crossover temperature, observed telegraphic noise in
the time domain due to random switching between the states provides their
lifetimes directly. We present a thermal model introducing a double-well
(bistable) feature with an intriguing quantity with respect to the devices'
temperature states. The effects of temperature fluctuations on the stability of
the states are shown. We discuss our results toward further improvement of the
efficiency of superconducting WL or nanowire single-photon detectors.
