Circuit QED signatures of Majorana bound states in semiconductor nanowires with spin-orbit-induced subband mixing

Circuit quantum electrodynamics (cQED) is a powerful toolset enabling the study of interaction between light and microscopic degrees of freedom in superconducting circuits. Recently, this toolset enabled resolving the spectrum of Andreev bound states (ABSs) in Josephson junctions based on III-V materials with strong spin-orbit coupling through their microwave transitions. Here, we consider such transitions in the topological regime with large external magnetic field, where more exotic Majorana bound states (MBSs) are predicted to appear. With detailed tight-binding simulations, we resolve the Andreev spectrum and examine how the cQED signatures of ABSs evolve from the known zero-field limit into the topological regime. We go beyond the conventional Lutchyn-Oreg model and consider multiple transverse modes and their spin-orbit-induced mixing. In this way, we find that MBSs originating from the lowest transverse mode mix with ABSs from higher modes deep in the topological regime. The subband mixing turns on microwave transitions involving MBSs, which would otherwise remain invisible. Our results point towards the possibility of direct cQED characterization of MBSs in a topological Josephson junction.