Influence of the ac Stark effect on multiphoton transitions in molecules

Abstract

A multiphoton mechanism for molecular beam transitions is presented which relies on a large first-order ac Stark effect to modulate the energy separation of the initial and final states of the multiphoton transition, but which does not require the presence of any intermediate level(s). The theoretical formalism uses ideas from the laser multiphoton literature for a two-level system interacting with a monochromatic electromagnetic radiation field, together with a close analog of the rotating wave approximation. The diagonal matrix elements of the Hamiltonian operator corresponding to the large ac Stark effect are removed by a mathematical substitution which in effect transforms appropriate differences of these diagonal elements into transition moments involving higher harmonics of the frequency of the monochromatic radiation field. The electric field strength of the true monochromatic radiation field is ‘‘distributed’’ among the higher harmonics of the effective field according to an expression involving Bessel functions. Because these Bessel functions are bounded, there exists for a given time t of exposure to the radiation, a threshold for the magnitude of the transition dipole matrix element coupling the two levels: Below this threshold, the transition probability in a traditional one-photon molecular beam electric resonance experiment cannot be made unity simply by increasing the amplitude of the radiation field. In fact, if the coupling matrix element is small enough, the molecular beam electric resonance signal cannot be detected within exposure time t. The algebraic formalism described above is checked by computer solution of an initial value problem involving four real coupled linear differential equations. It is then used to explain the multiphoton transitions previously observed in molecular beam electric resonance studies on the two symmetric top molecules OPF3 and CH3 CF3, where the number of photons involved in a given transition varies from 1–40. Application of the analysis to other experiments is briefly discussed.