Dynamics of quasiparticle trapping in Andreev levels

We present a theory describing the trapping of a quasiparticle in a prototypical Josephson junction, a single-channel superconducting weak link. We calculate the trapping and untrapping rates associated to absorption and emission of both photons and phonons. We show that the presence of an electromagnetic mode with frequency smaller than the gap gives rise to a rather abrupt transition between a fast-relaxation regime dominated by coupling to photons and a slow-relaxation regime dominated by coupling to phonons. This conclusion is illustrated by the analysis of a recent experiment [Zgirski, Bretheau, Le Masne, Pothier, Esteve, and Urbina, Phys. Rev. Lett. 106, 257003 (2011)] measuring the dynamics of quasiparticle trapping in a superconducting atomic contact coupled to a Josephson junction. With realistic parameters, the theory provides a semiquantitative description of the experimental results.