  The direct effect of an axion field on Josephson junctions is analyzed
through the consequences on the effective potential barrier that prevents the
junction from switching from the superconducting to the finite-voltage state.
We describe a method to reliably compute the quasipotential with stochastic
simulations, which allows to span the coupling parameter from weakly
interacting axion to tight interactions. As a result, we obtain that the axion
field induces a change in the potential barrier, therefore determining a
significant detectable effect for such a kind of elusive particle.
