Quantum Ising dynamics and Majorana-like edge modes in the Rabi lattice model

TL;DR

This paper explores the quantum Ising dynamics and Majorana-like edge modes in the Rabi lattice model, revealing their properties, signatures, and stability through theoretical analysis and DMRG simulations.

Contribution

It demonstrates the emergence of quantum Ising behavior and Majorana-like edge modes in the Rabi lattice, providing observable signatures and conditions for their protection.

Findings

Quantum Ising dynamics appear in the Rabi lattice at strong coupling.

End-to-end dipole correlation relates to spontaneous polarization as a signature.

Conditions for protecting edge modes against perturbations are identified.

Abstract

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.