  The atomic dipoles in the Rabi lattice model exhibit quantum Ising dynamics
in the limit of strong atom-photon interaction. It governs the para- to
ferro-electric phase transition in the ground state. On an open chain, it
implies the existence of two Majorana-like, albeit topologically unprotected,
edge modes in the ordered phase. The relation \rho^x_{1L}=p^8 between the
end-to-end dipole correlation, \rho^x_{1L}, and the spontaneous polarization,
p, is proposed as an observable signature of these edge modes. The DMRG
calculations on the one-dimensional Rabi lattice support the strong coupling
quantum Ising behavior, and correctly yield the proposed end-to-end dipole
correlation. The conditions which protect the edge modes against the adverse
perturbations are also identified.
