Numerical versus analytical models of laser-induced population redistribution in Rydberg atoms

Abstract

Our recent approximate analytical results on the evolution of the initial state and the excitation from this state of a band of high Rydberg states by an optical pulse @Phys. Rev. A 55, 2144 ~1997!# are compared with more exact numerical results. The difference between the two approaches is that the approximations of representative atom-field couplings and equidistant spacing of high Rydberg states, applied in the analytical model, are removed in the numerical model. We find that the approximate analytical model is not able to reproduce all the results of the more exact numerical model, if the laser pulse is very short ~i.e., much shorter that the Kepler period of the resonantly excited high Rydberg state! or very intense ~i.e., when the Rabi period for the resonant transition is substantially shorter than the above Kepler period!. This mainly concerns the redistribution of the population over different Rydberg states. The analytical model predicts a symmetric distribution centered around the resonantly excited Rydberg state, irrespective of the pulse duration and intensity, while the numerical model allows an asymmetric distribution with its maximum shifted towards lower Rydberg states. Despite the above-stated difference, the analytical model is able to give preliminary results for the total population of all the excited Rydberg states and the evolution of the initial state, imitating at least qualitatively the results of the numerical model in certain time and intensity scales. @S1050-2947~99!06301-5#