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 matrix-product 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 on-going experimental investigations of nanowire-based
superconducting qubits.
Planar josephson junctions fabricated with magnesium diboride films
