POPULATION TRANSFER AT PERIODICALLY REPEATED LEVEL-CROSSINGS

We have explored a genuinely time-dependent problem consisting of periodic crossings of energy levels. The model can be realized in several physical systems, but we refer it explicitly to a two-level ion that swings in a harmonic trap and concurrently interacts with a traveling light wave. We have solved the Schrodinger equation for this model by numerical integration as well as by the use of matrix continued fractions for the steady state. We investigate both the time and the frequency behavior of the model. We have also compared the exact behavior with an intuitive model based on a Landau-Zener description of each crossing followed by a simple relaxation behavior. In addition, the coherent interaction with the field is found to lead to a resonancelike behavior of the population transfer, which we can attribute to the accumulated phase of the Bloch vector. The various time scales of the problem are identified and their physical significance is elucidated.