For an atom or molecule in which two transitions are driven by laser beams, a three‐state model is used. Transitions among the three states are caused only by the oscillating electric fields of the laser beams. The amplitudes and detunings of the two laser beams, which are various functions of the time, appear in the Schrödinger equation for the atom or molecule. In certain cases, the Schrödinger equation can be solved analytically, to find transition probabilities and the probability of no transition. This is done by using Clausen’s special function, or by assuming that the sum of the two detunings is zero at all times. Conditions for complete transfer of the population from the ground state to an excited state are obtained from the analytic solutions.
Carroll, C. E. and Hioe, Foek T. (1988). "Driven 3-State Model and Its Analytic Solutions." Journal of Mathematical Physics 29.2, 487-509.
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