Braiding of Majorana Fermions in a Cavity

We study the dynamical process of braiding Majorana bound states (MBS) in the presence of the coupling to photons in a microwave cavity. We show theoretically that the π/4 phase associated with the braiding of MBS, as well as the parity of the ground state are imprinted into the photonic field of the cavity, which can be detected by dispersive readout techniques [1]. We use a density matrix description for the dynamics of the low energy states in order to account for various relaxation channels both in the adiabatic regime, as well as within the Floquet formalism in the case of periodic driving. We evaluate the average photon number and the second order photon coherence function g⁽²⁾(0), and show they are affected by the non Abelian Berry phase accumulated during the braiding process [2]. These manifestations are purely dynamical, they occur in the absence of any splitting of the MBS that are exchanged, and they disappear in the static setups studied previously. Conversely, the cavity can affect the braiding phase, which in turn should allow for cavity controlled braiding.

[1] Mircea Trif and Pascal Simon, Phys. Rev. Lett. 122, 236803 (2019).
[2] Mircea Trif and Pascal Simon, Adv. Quantum Technol., in press (2019).