Superradiant phase transition induced by the indirect Rabi interaction

We theoretically study the superradiant phase transition (SPT) in an indirect Rabi model, where both a two-level system and a single mode bosonic field couple to an auxiliary bosonic field. We find that the indirect spin-field coupling induced by the virtual excitation of the auxiliary field can allow the occurrence of a SPT at a critical point, and the influence of the so-called $A^2$ term in the normal Rabi model is naturally avoided. In the large detuning regime, we present the analytical expression of quantum critical point in terms of the original system parameters. The critical atom-field coupling strength is tunable, which will loosen the conditions on realizing the SPT. Considering a hybrid magnon-cavity-qubit system, we predict the squeezed cat state of magnon generated with feasible experimental parameters, which has potential applications in quantum metrology and quantum information processing.