Report on scipost_201906_00002v1

Abstract

We study nanowire-based Josephson junctions shunted by a capacitor and take into account the presence of low-energy quasiparticle excitations. These are treated by extending conventional models used to describe superconducting qubits to include the coherent coupling between fermionic quasiparticles, in particular the Majorana zero modes that emerge in topological superconductors, and the plasma mode of the junction. Using accurate, unbiased matrixproduct state techniques, we compute the energy spectrum and response function of the system across the topological phase transition. Furthermore, we develop a perturbative approach, valid in the harmonic limit with small charging energy, illustrating how the presence of low-energy quasiparticles affects the spectrum and response of the junction. Our results are of direct interest to ongoing experimental investigations of nanowire-based superconducting qubits. 5.2 Non-perturbative couplings 18 6 Conclusions and Outlook 21 A Tight-binding model 22 B Extracting E M 23 C Numerical results in the harmonic limit 24 References 24