Microwave signatures of Majorana states in a topological Josephson junction

We find the admittance of a topological Josephson junction Y( omega ,[phi]0,T) as a function of frequency omega , the static phase bias [phi]0 applied to the superconducting leads, and temperature T. The dissipative part of Y allows for spectroscopy of the subgap states in the junction. The resonant frequencies omega M,n([phi]0) for transitions involving the Majorana (M) doublet exhibit characteristic kinks in the [phi]0 dependence at [phi]0=[pi]. The kinks, associated with decoupled Majorana states, remain sharp and the corresponding spectroscopic lines are bright at any temperature, as long as the leads are superconducting. The developed theory may help with regard to extracting quantitative information about Majorana states from microwave spectroscopy.