  A Josephson junction subject to an external RF excitation may experience the
inverse AC Josephson effect, where the phase across the junction locks to the
drive. The resulting ``Shapiro steps'' of quantized voltage are currently
utilized in primary voltage standards. The effect has also been a key technique
in the search for topological superconductivity. Here, we study a particularly
interesting regime in which the zero voltage state becomes unstable at zero DC
bias, and the junction spontaneously develops the first Shapiro step with a
voltage $V=\pm \hbar \omega /2e$. The switching time between the $+ \hbar
\omega /2e$ and $- \hbar \omega /2e$ states ranges from milliseconds to hours.
Most interestingly, we find a surprising regime with a non-monotonic
temperature dependence, in which the switching time demonstrates a pronounced
minimum at intermediate temperatures. Tuning of the measurement parameters is
also shown to give rise to a tristable switching behavior, showcasing the
potential for further experiments in stochastic physics and quantum
thermodynamics.
