  We define the anisotropic Rabi model as the generalization of the spin-boson
Rabi model: The Hamiltonian system breaks the parity symmetry; the rotating and
counter-rotating interactions are governed by two different coupling constants;
a further parameter introduces a phase factor in the counter-rotating terms.
The exact energy spectrum and eigenstates of the generalized model is worked
out. The solution is obtained as an elaboration of a recent proposed method for
the isotropic limit of the model. In this way, we provide a long sought
solution of a cascade of models with immediate relevance in different physical
fields, including i) quantum optics: two-level atom in single mode cross
electric and magnetic fields; ii) solid state physics: electrons in
semiconductors with Rashba and Dresselhaus spin-orbit coupling; iii) mesoscopic
physics: Josephson junctions flux-qubit quantum circuits.
