Bloch oscillations in nanoscale Josephson junctions with a Coulomb charging energy comparable to the Josephson coupling energy are explored within the context of a model previously considered by Geigenm\"uller and Sch\"on that includes Zener tunneling and treats quasiparticle tunneling as an explicit shot-noise process. The dynamics of the junction quasicharge are investigated numerically using both Monte Carlo and ensemble approaches to calculate voltage--current characteristics in the presence of microwaves. We examine in detail the origin of harmonic and subharmonic Bloch steps at dc biases I=(n/m)2ef induced by microwaves of frequency f and consider the optimum parameters for the observation of harmonic (m=1) steps. We also demonstrate that the GS model allows a detailed semi-quantitative fit to experimental voltage--current characteristics previously obtained at the Chalmers University of Technology, confirming and strengthening the interpretation of the observed microwave-induced steps in terms of Bloch oscillations.
@article{arxiv.1703.06996,
title = {Modeling Bloch Oscillations in Nanoscale Josephson Junctions},
author = {Heli Vora and R. L. Kautz and S. W. Nam and J. Aumentado},
journal= {arXiv preprint arXiv:1703.06996},
year = {2017}
}