General formulation of locally designed coherent control theory for quantum system

Abstract

A general local control theory for manipulating quantum system dynamics is developed. Basic concept of the present theory is lying in the realization of monotonous increasing condition of the performance index, which is locally (in time domain) defined to major how the present quantum state satisfies the current objective. The local control field is designed to satisfy the above condition taking into account the equation of motion of the system. It is found, through the formulation, that the monotonous increasing condition can be achieved as long as the performance index is given as a function of expectation values of time-dependent observable operators, whose equation of motion is governed by the field-free system Hamiltonian or Liouvillian. It is also shown that the present theory is a generalization of the local optimization approach which has been successfully applied to many of molecular dynamics control problems. As for the special cases, performance indices for “transition path control,” “population distribution control,” and “wave packet shaping” are proposed. The theory is applied to vibrational control problems of the one-dimensional model system of hydrogen fluoride. The results show that the present method works effectively for the population dynamics control as well as the wave packet shaping.