  We introduce the anisotropic two-photon Rabi model in which the rotating and
counter rotating terms enters along with two different coupling constants.
Eigenvalues and eigenvectors are studied with exact means. We employ a
variation of the Braak method based on Bogolubov rotation of the underlying
$su(1,1)$ Lie algebra. Accordingly, the spectrum is provided by the analytical
properties of a suitable meromorphic function. Our formalism applies to the
two-modes Rabi model as well, sharing the same algebraic structure of the
two-photon model. Through the analysis of the spectrum, we discover that the
model displays close analogies to many-body systems undergoing quantum phase
transitions.
