Control of topological properties in the Kitaev chain by quantum microwave radiation

We investigate observable signatures coming from the light-matter coupling of a Kitaev chain embedded in a microwave cavity.
We study and describe the quantum phases of the system, and the transitions between them, for two different composite fermion-photon model, namely a cavity homogeneously coupled to the whole chain as well as the case of a microwave selectively coupled to an edge site of the chain only. Our results are based on two complementary approaches, an analytic mean-field theory and numerical matrix product state simulations. We find that as a consequence of the interaction between the matter-radiation subsystems, a topological non-trivial phase of the Kitaev chain can be increased and identified by following the behavior of different photon observables such as the mean photon number and the Fano factor. Our analysis reveals a second order phase transition for different types of microwave-fermion couplings. The observed phenomena and the control of the quantum state of the chain assessed with the cavity, make it a potential candidate for further experimental investigations that seek the presence of Majorana fermions in solid-state systems.