  Hybrid nanowires with proximity-induced superconductivity in the topological
regime host Majorana zero modes (MZMs) at their ends, and networks of such
structures can produce topologically protected qubits. In a double-island
geometry where each segment hosts a pair of MZMs, inter-pair coupling mixes the
charge parity of the islands and opens an energy gap between the even and odd
charge states at the inter-island charge degeneracy. Here, we report on the
spectroscopic measurement of such an energy gap in an InAs/Al double-island
device by tracking the position of the microwave-induced quasiparticle (qp)
transitions using a radio-frequency (rf) charge sensor. In zero magnetic field,
photon assisted tunneling (PAT) of Cooper pairs gives rise to resonant lines in
the 2e-2e periodic charge stability diagram. In the presence of a magnetic
field aligned along the nanowire, resonance lines are observed parallel to the
inter-island charge degeneracy of the 1e-1e periodic charge stability diagram,
where the 1e periodicity results from a zero-energy sub-gap state that emerges
in magnetic field. Resonant lines in the charge stability diagram indicate
coherent photon assisted tunneling of single-electron states, changing the
parity of the two islands. The dependence of resonant frequency on detuning
indicates a sizable (GHz-scale) hybridization of zero modes across the junction
separating islands.
