  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.
