Quantum dynamics of atoms in modulated laser fields

Abstract

Solutions of the Schrodinger equations are obtained, in terms of Bessel, Legendre, and hypergeometric functions, for the transition amplitudes of two-, three-, four- and N-level atoms in amplitude- and frequency-modulated laser fields. Exact solutions for the atom evolution parameters are obtained in those cases when the Hamiltonian of the interaction of the quantum system with the classical fields has exact symmetries such as dynamic so2 and so3,1 Lie algebras and isomorphic ones. In the case of broken symmetry the solutions take the form of series in terms of a small dimensionless quantity and can be obtained in principle in arbitrary order of smallness in the variable. A regular procedure for finding the solutions of the Schrodinger and Bloch matrix equations is developed, based on their dynamic symmetries and on the calculations of the respective group parameters that determine the dynamics of the atoms in modulated laser fields.