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

Our recent approximate analytical results on the evolution of the initial s tate 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 exa ct numerical results. The difference between the two approaches is that the approximations of representative atom-field couplings and equidistant spac ing 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 th e resonantly excited high Rydberg state) or very intense (i.e., when the Ra bi period for the resonant transition is substantially shorter than the abo ve Kepler period). This mainly concerns the redistribution of the populatio n over different Rydberg states. The analytical model predicts a symmetric distribution centered around the resonantly excited Rydberg state, irrespec tive of the pulse duration and intensity, while the numerical model allows an asymmetric distribution with its maximum shifted towards lower Rydberg s tates. Despite the above-stated difference, the analytical model is able to give preliminary results for the total population of all the excited Rydbe rg states and the evolution of the initial state, imitating at least qualit atively the results of the numerical model in certain time and intensity sc ales. [S1050-2947(99)06301-5].