Microwave signatures of Z2 and Z4 fractional Josephson effects

Fractional Josephson effects comprise some of the main signatures of topological features and quasi-particle fractionalization in Josephson junctions.

With the goal of better understanding the effects of interactions, as well as of developing new methodologies for extracting such topological information from Josephson junctions, we present a many-body exact diagonalization study of the Z2 and Z4 Josephson effects in circuit quantum electrodynamics architectures. After an introduction to the rich phenomenology of these Josephson effects, I will present numerical simulations conducted on Kitaev

chain Josephson junctions hosting nearest-neighbour Coulomb interactions.

The low-energy effective theory of highly transparent Kitaev chain junctions is shown to be identical to that of junctions

created at the edge of a quantum spin-Hall insulator. By capacitively coupling the interacting junction to a microwave resonator, we predict signatures of the fractional Josephson effects on the cavity frequency and on time-resolved reflectivity measurements.