  We show that the microwave (MW) spectra in semiconductor-nanowire-based
transmon qubits provide a strong signature of the presence of Majorana bound
states in the junction. This occurs as an external magnetic field tunes the
wire into the topological regime and the energy splitting of the emergent
Majorana modes oscillates around zero energy owing to their wave function
spatial overlap in finite-length wires. In particular, we discuss how these
Majorana oscillations, and the concomitant fermion parity switches in the
ground state of the junction, result in distinct spectroscopic features --in
the form of an intermitent visibility of absorption lines-- that strongly
deviate from standard transmon behavior. In contrast, non-oscillating zero
modes, such as topologically trivial Andreev bound states resulting from
sufficiently smooth potentials, exhibit an overall standard transmon response.
These differences in the MW response could help determine whether the junction
contains topological Majoranas or not.
