The Properties and Light-Matter Interaction of a Superconducting Majorana-Transmon Qubit

We analyse the transmon regime Hamiltonian of a Cooper-Pair-Box where the superconducting phase difference is coupled to the zero energy parity states that arise from Majorana quasi-particles. We investigate the level structure and properties of the transmon qubit in this regime where even a small coupling causes hybridization of different transmon-parity states without compromising the suppression of charge dispersion. We show that the microwave photon-qubit coupling is sensitive to the gate bias and all the energy scales of the Hamiltonian. As well as a probe for topological-superconductor excitations, we propose that this type of device could be used to realise a high coherence tunable four-level system in the superconducting circuits architecture.