No experiment could directly test the particle/antiparticle duality of Majorana fermions, so far. However, this property represents a necessary ingredient towards the realization of topological quantum computing schemes. Here, we show how to complete
this task by using microwave techniques. The direct coupling between a pair of overlapping Majorana bound states and the electric field from a microwave cavity is extremely difficult to detect due to the self-adjoint character of Majorana fermions which forbids direct energy exchanges with the cavity. We show theoretically how this problem can be circumvented by using photo-assisted tunneling to fermionic reservoirs. The absence of direct microwave transition inside the Majorana pair in spite of the light-Majorana coupling would represent a smoking gun for the Majorana self-adjoint character.
Understanding the interaction between cavity photons and electronic nanocircuits is crucial for the development of Mesoscopic Quantum Electrodynamics (QED). One has to combine ingredients from atomic Cavity QED, like orbital degrees of freedom, with
tunneling physics and strong cavity field inhomogeneities, specific to superconducting circuit QED. It is therefore necessary to introduce a formalism which bridges between these two domains. We develop a general method based on a photonic pseudo-potential to describe the electric coupling between electrons in a nanocircuit and cavity photons. In this picture, photons can induce simultaneously orbital energy shifts, tunneling, and local orbital transitions. We study in details the elementary example of a single quantum dot with a single normal metal reservoir, coupled to a cavity. Photon-induced tunneling terms lead to a non-universal relation between the cavity frequency pull and the damping pull. Our formalism can also be applied to multi quantum dot circuits, molecular circuits, quantum point contacts, metallic tunnel junctions, and superconducting nanostructures enclosing Andreev bound states or Majorana bound states, for instance.
