Resonance excitation effect for a molecule driven by a laser radiation field: Algebraic dynamics method to determine the diabatic energy levels and geometric phase

Using the method of algebraic dynamics, we investigate the hω(4) non-autonomous quantum system, which is formed by a single molecule within a harmonic potential driven by laser radiation field and obtain the exact solutions of the system. Based on the exact solutions, in particular on the features of the diabatic energy levels, then we proceed to studying the geometric phase of the system. From the above results, we may determine the vibration frequency of the molecule by measuring the changes in the properties of geometric phase.