A generalized approach to the control of the evolution of a molecular system

Abstract

The theory of active control of molecular motion by use of shaped laser pulses is developed emphasizing the role of interference and using thermodynamic analogies. Attention is focused on the control of the dynamics in a system with n states coupled by radiation, and the phase relations which generate particular control schemes are derived. Among the new results reported is an optimal control scheme which constrains the value of the phase. The n-state model can be considered to represent a molecule with n electronic potential energy surfaces and an arbitrary number of degrees of freedom or as the skeleton spectrum of system where each level in the spectrum can be associated with a specific set of quantum numbers for all of the degrees of freedom. We show how the control of the dynamics of an n-state molecule can be represented in terms of the control of the dynamics of a precisely defined surrogate fewer state system. This reduction is illustrated by use of a surrogate two state system to describe the dynamics of population transfer in a three state system.