  We employ a polaron picture to investigate the properties of the two-photon
quantum Rabi model (QRM), which describes a two-level or spin-half system
coupled with a single bosonic mode by a two-photon process. In the polaron
picture, the coupling in the two-photon process leads to spin-related asymmetry
so that the original single bosonic mode splits into two separated frequency
modes for the opposite spins, which correspond to two \textit{bare} polarons.
Furthermore, the tunneling causes these two bare polarons to exchange their
components with each other, thus leading to additional \textit{induced}
polarons. According to this picture, the variational ground-state wave function
of the two-photon QRM can be correctly constructed, with the ground-state
energy and other physical observables in good agreement with the exact numerics
in all the coupling regimes. Furthermore, generalization to multiple induced
polarons involving higher orders in the tunneling effect provides a systematic
way to yield a rapid convergence in accuracy even around the difficult spectral
collapse point. In addition, the polaron picture provides a distinctive
understanding of the spectral collapse behavior, that is about the existence of
discrete energy levels apart from the collapsed spectrum at the spectral
collapse point. This work illustrates that the polaron picture is helpful to
capture the key physics in this nonlinear light-matter interaction model and
indicates that this method can be applicable to more complicated QRM-related
models.
