CONTROLLABILITY OF QUANTUM SYSTEMS FOR THE MORSE AND PT POTENTIALS WITH DYNAMIC GROUP SU(2)

Abstract

1. Introduction With the revolution of the microelectronic processing power, the study of the quantum control theory for the manipulation of a quantum system state has attracted much attention of many authors [636-676]. Almost all of these studies are motivated by the recent advances in the field of the nuclear magnetic resonance and laser spectroscopy, e.g., the quantum control by laser pulse can now be realized experimentally [638]. Recently, Ramakrishna and Rabitz have of a molecule with a given Hamiltonian through a unitary operator representing quantum evolution [639]. In addition, the nondegenerate quantum control problem has been solved analytically by [640]. The quantum state control via tunnelling in a double-well optical potential has been reported [641]. It is shown by these works that the quantum control has been widely applied to molecular and atomic physical problems and that much attention has been paid to the problem of a quantum system with nondegenerate eigenstates. The reasons why the great efforts have been made in this field are the following. First, it is possible to understand the basic physics associated with the quantum structures such as the quantum fluctuation and other quantum effects and to explore their controllability and design new species of useful devices. Therefore, the investigation in this recently sprung up field becomes exciting and potential. Second, the quantum control is a kind of underlying technology which makes quantum computation possible. In turn, the quantum information processing may provide the quantum control with many novel techniques for performing feedback and state estimation with possible applications to 225 computation by DiVincenzo [637], the investigation of quantum control has shown how sequences of short laser pulses can be applied to control the state been the subject of interest [636]. Since the pioneering work on the quantum