Parity symmetry and parity breaking in the quantum Rabi model with addition of Ising interaction

We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [J. Phys. A 46, 265302 (2013)], we consider a physically realistic method by involving an additional spin into the quantum Rabi model to couple with the original spin by an Ising interaction. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom. Experimental feasibility of realizing the models under discussion is investigated.