Microwave transitions as a signature of coherent parity mixing effects in the Majorana-transmon qubit

Solid-state Majorana fermions are generating intensive interest because of their unique properties and possible applications in fault tolerant quantum memory devices. Here we propose a method to detect signatures of Majorana fermions in hybrid devices by employing the sensitive apparatus of the superconducting charge-qubit architecture and its efficient coupling to microwave photons. In the charge and transmon regimes of this device, we find robust signatures of the underlying Majorana fermions that are, remarkably, not washed out by the smallness of the Majorana contribution to the Josephson current. It is predicted that at special gate bias points the photon-qubit coupling can be switched off via quantum interference, and in other points it is exponentially dependent on the control parameter E-J/E-C. We propose that this device could be used to manipulate the quantum state of the Majorana fermion and realize a tunable high coherence four-level system in the superconducting-circuit architecture.