Two-photon resonance in three-state model driven by two laser beams

A simple model with only three quantum states is used for an atom or molecule in which two transitions are driven by two overlapping laser pulses. The amplitudes of the two pulses are not proportional to the same function of time. The authors impose the 'two-photon resonance' condition, but the two pulses separately are not applied at the resonant frequencies. For pulse pairs having certain shapes, the wavefunctions are written in terms of generalised hypergeometric functions. Simple formulae for transition probabilities are then obtained, are are used to discuss transfer of the three-state system from its ground state to its highest state.