2-LEVEL SYSTEM IN A GAUSSIAN FIELD - AN APPROXIMATE SOLUTION

The problem of the evolution of a two-level quantum system in a radiation field of Gaussian shape with detuning is addressed by seeking an approximate expression for the transformation function governing the interaction. The transformation operator requires the evaluation of two independent matrix elements: the former is obtained by the Rosen-Zener conjecture; the latter is based on an expansion using the main parameters involved in the first one. The expressions obtained, which are supposed to hold in the case of small detunings, have been tested by comparison with a numerical integration. Then the solutions are modified to take into account decay phenomena to other levels. As a final example, the expressions dealing with the transition probability in the case of two separated oscillatory fields are given.