Why macroscopic quantum tunnelling in Josephson junctions differs from tunnelling of a quantum particle

Abstract

We show that the macroscopic quantum tunnelling of a fluxon in a Josephson junction cannot be described, even qualitatively, as the tunnelling of a quantum particle in a potential U(φ), where the phase difference φ plays the role of particle position, if the length of the junction d exceeds a fluxon length. We calculate the probability per unit time of tunnelling (or escape rate), Γ, which has a form Γ=A exp(-B). In contrast to particles, where the B is proportional to d, our field-theory predicts a different behavior of B for either usual, 0–π, or stacks of Josephson junctions, giving rise to a renormalization of Γ by many orders of magnitude.