We present a detailed and exact construction of a unitary operator accomplishing the diagonalization of an effective quadratic radiation-matter interaction model describing a bidimensionally trapped and appropriately laser-driven ion. The possibility of applying the same mathematical method to other effective radiation-matter interaction model is briefly put into evidence.
Maniscalco, S., Messina, A., & Napoli, A. (2001). Symmetry-based canonical dressing of a bidimensionally trapped and laser-driven ion. Reports on Mathematical Physics, 48(1-2), 167-174. https://doi.org/10.1016/S0034-4877(01)80076-8