Step-by-step method in adiabatic Floquet theory for laser pulses

Article type: Research Article

Authors: Shtoff, Alexander V.^a | Rérat, Michel^b

Affiliations: [a] Department of Quantum Mechanics, S.Petersburg State University, S. Petersburg, St. Petergof, Ulianovskaya, 1, Russia. E-mail: shtoff@transkeino.ru | [b] Equipe de Chimie-Physique, IPREM FR2606, UMR 5254, Universite' de Pau, 64000 Pau, France. E-mail: michel.rerat@univ-pau.fr

Abstract: A new step-by-step technique of solving the time-dependent Schrödinger equation for quantum systems driven by chirped laser pulses is developed. Our approach is based on application of the adiabatic theorem of quantum mechanics to instantaneous Floquet states in an extended Hilbert space and on approximation of the slowly varying pulse parameters by step functions. This approximation and representation of the evolution operator in the form of T-ordered product of operators acting at short time intervals make it possible to reveal a correlation between the proposed method and the iterative solution of the Schrödinger equation. By example of a two-level system, the rate of the step-by-step procedure convergence with respect to decreasing of a short time step is analyzed. Applicability of proposed computational procedure is demonstrated by example of Landau-Zener transition probabilities calculation using the Dykhne-Davis-Pechukas formula and by means of the step-by-step method. The developed strategy is applied to describe the response of N-level system under the action of pulse radiation. It is used to calculate final non-adiabatic electronic transitions probabilities, energy levels populations and the field-corrected polarizability of LiH molecule. The contribution of electronic states to the dynamic field-corrected polarizability is analyzed.

DOI: 10.3233/JCM-2008-81-205

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 8, no. 1-2, pp. 119-137, 2008