Symmetry conjugates and dynamical properties of the quantum Rabi model

Abstract

Symmetry transformations have proved useful in determining the algebraic structure and internal dynamical properties of physical systems. In the quantum Rabi model, invariance under parity symmetry transformation has been used to obtain exact solutions of the eigenvalue equation and very good approximations of the internal dynamics of the interacting atom-light system. In this article, two symmetry operators, characterized as “duality” symmetry operators, have been introduced which transform the quantum Rabi Hamiltonian into duality conjugates. Symmetric or antisymmetric linear combinations of the Rabi Hamiltonian and a corresponding duality conjugate yield exact forms of the familiar spin-dependent force driven bosonic , coupling-only or quantized light mode quadrature-driven fermionic Hamiltonian. Exact solutions of the dynamics generated by these simpler forms of QRM Hamiltonian provide nonclassical states such as the Schroedinger cat states which reveal fundamental quantum features usual observed in experiments.