Abstract
The response of an atom to the action of a pulse shorter than the Kepler period of the optically-active electron is often treated analytically using the sudden-perturbation approximation (SPA). It relies on the truncation of the evolution operator expansion in a series over the dimensionless parameter ε sys τ L, where ε sys is the system-dependent characteristic energy and τ L is the pulse duration. We examine the SPA with the use of a basis-based solution of the time-dependent Schrödinger equation (TDSE) for the case of a hydrogen atom interacting with two different types of ultrashort pulses, a half-cycle pulse and a few-cycle pulse. The length-gauge form of the electron-field interaction potential is used. The SPA transition probabilities are shown to deviate slightly but systematically from the correct values for the positive-energy states in the region where the sudden-perturbation condition is violated. It is shown that the SPA expectation value of the electron displacement as a function of time differ qualitatively from what follows from the ab initio TDSE solution. Nevertheless, the SPA is shown to be a good approximation for the description of the expectation value of the electron momentum.
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Lugovskoy, A., Bray, I. Sudden perturbation approximations for interaction of atoms with intense ultrashort electromagnetic pulses. Eur. Phys. J. D 69, 271 (2015). https://doi.org/10.1140/epjd/e2015-60471-2
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DOI: https://doi.org/10.1140/epjd/e2015-60471-2