A Josephson junction may be in a stable odd parity state when a single quasiparticle is trapped in an Andreev bound state. Embedding such junction in an electromagnetic environment gives rise to a special quantum mechanics of superconducting phase that we investigate theoretically. Our analysis covers several representative cases, from the lifting of the supercurrent quench due to quasiparticle poisoning for a low ohmic impedance of the environment, to a Schmid transition in a current-biased junction that for odd parity occurs at four times bigger critical impedance. For intermediate impedances, the supercurrent in the odd state is higher than in the even one.
@article{arxiv.2309.02728,
title = {Josephson quantum mechanics at odd parity},
author = {Manuel Houzet and Julia S. Meyer and Yuli V. Nazarov},
journal= {arXiv preprint arXiv:2309.02728},
year = {2023}
}