Topological protection of Majorana polaritons in a cavity

Cavity embedding is an emerging paradigm for the control of quantum matter, offering avenues to manipulate electronic states and potentially drive topological phase transitions. In this work, we address the stability of a onedimensional topological superconducting phase to the vacuum quantum fluctuations brought by a global cavity mode. By employing a quasiadiabatic analytical approach completed by density matrix renormalization group calculations, we show that the Majorana end modes evolve into composite polaritonic modes while maintaining the topological order intact and robust to disorder. These Majorana polaritons keep their non-Abelian exchange properties and protect a twofold exponentially degenerate ground state for an open chain. They become, however, weak edge modes in the sense that they no longer commute with the full Hamiltonian and protect the exponential degeneracy only in the ground-state manifold.