Quantum phase slips in a resonant Josephson junction

We investigate the consequences of resonant tunneling of Cooper pairs on the quantum phase slips occurring in a Josephson junction. The amplitude for quantum tunneling under the Josephson potential barrier is modified by the Landau-Zener amplitude to excite an Andreev bound state, resulting in the suppression of $2\pi$ phase slips. As a consequence, close to resonance, $4\pi$ phase slips become the dominant tunneling process. We illustrate this crossover by determining the energy spectrum of a transmon circuit, showing that a residual charge dispersion persists even at perfect transparency.