Abstract

A strong laser field interacting with an atom or a molecule can induce a coherent process which includes a large number of energy levels. If we can find a transformation which eliminates the explicit time dependence of the interaction Hamiltonian (for example, the rotating-wave approximation), we can reduce the dynamic problem to the consideration of eigenvalues and eigenvectors of the Hamiltonian. However, the complexity of an arbitrary multilevel Hamiltonian usually forces us to use numerical methods, and, therefore, not much general understanding about multilevel systems can be achieved. We consider the multilevel problems in a more general setting. Our approach is based on the observation that an arbitrary Hamiltonian matrix can be transformed into a tridiagonal form by unitary transformation.¹ A tridiagonal form represents a ladder-type multilevel system. From all W-level systems the ladder configuration is the simplest in the sense that the number of level connections is the smallest possible. This means that the most effective analysis of a given multilevel system can be achieved using the transformation to ladder configuration. The spectral analysis of ladders is facilitated by the connections to orthogonal polynomials and continued fractions. The investigations about the spectral properties of ladders are reported.

© 1988 Optical Society of America