Algebraic treatment of some systems with spin-like interactions with applications in quantum optics and vibronic spectroscopy

International audienceA unified scheme based on algebraic techniques is proposed to solve the eigenvalue equation for a class of systems involving spin-like interactions. From general assumptions Hamiltonian models are built from selected elements in the enveloping algebra of the harmonic oscillator, su(2) and su(1, 1) algebras. Our method is next illustrated through examples taken in the areas of quantum optics and dynamical Jahn-Teller systems in orbital doublets