A class of pulse functions is found for which analytic solutions to the problem of two levels coupled by these pulse functions is obtained. The hyperbolic-secant coupling pulse is included in this class of functions leading to the Rosen-Zener solution, but all other pulses belonging to the class function are asymmetric. The asymmetric pulses lead to qualitatively new features in the solutions; in general, it is impossible to have a zero-transition probability with such asymmetric pulses.
We have studied a special class of time-symmetric pulses interacting with a two-level system. These pulses are built out of a class of asymmetric functions for which the analytic description of the interaction was possible. The time behavior of these pulses is given. We have evaluated the transition probability in a closed form. These pulses can be used to simulate the familiar Lorentzian and Gaussian pulse shapes remarkably well. Therefore, they can be used in computing the overall features of the interaction process. Comparisons of the transition amplitudes are made between the closed-form solution and numerically calculated Lorentzian and Gaussian cases.
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