Transition probability of a two-level atom interacting with a time-symmetric pulse

Abstract

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.