The Optimal Control Of Quantum Pathways In Closed Systems And Their Encoding Methods In Open Systems

Quantum pathways describe the details of quantum dynamics.It is an important tool to investigate the control mechanisms and thus meaningful in physics.The study of closed multi-level systems explore how to improve the population transfer from the initial state to the target state from the viewpoint of interference of different quantum pathways.The information of quantum pathways in closed and open systems can both be extracted in the framework of Hamiltonian-encoding and Observable-decoding(HE-OD).In closed systems,the encoding scheme is simple due to the lack of environment.The pathway amplitudes from HE-OD and Dyson integration are consistent.For open systems,the dynamics is described in the Liouville space instead of the Hilbert space.The environment effect will appear both in the diagonal and off-diagonal elements in the system Hamiltonian.The normal encoding scheme used in closed systems will lead to the inconsistent results of pathway amplitudes.So our thesis compares and analyzes the difference and relation between pathway amplitudes by the two method,and then proposes a new encoding scheme,which can avoid the self-to-self "non-physical"transitions induced by HE-OD smartly,and at the same time make the HE-OD result consistent with the Dyson integration's.The contents are:1.Lee's eight-block scheme gives a solution for a four-level system to maximize the two-photon absorption(TPA).The number of blocks is closely related to the energy and dipole structures of the system,and the block boundaries are the roots of a polynomial equation.In this work,we prove that there are always two real roots when we extend Lee's scheme to a five-level system with three TP A pathways,which leads to a twelve-block control scheme.We also propose a new block scheme,which is proved to be global optimal.The new block scheme can improve TP A effectively compared with transform limited(TL)pulses.This research is in Chapter Two.2.The HE-OD methodology in the open system is discussed.The pathway amplitude obtained from this method is compared with that by the Dyson integration.The difference is analyzed and a new encoding scheme is proposed to encoding some diagonal elements in the Hamiltonian to reduce the difference.However the new scheme induces some self-to-self transitions,like|11>>?|11>>,|22>>?|22>>and |33>>?|33>>,which have no physical meaning.This research is in Chapter Three.3.A new systematic method is proposed to avoid these self-to-self pathways.This chapter wants to try to analysis the reasons under the phenomenon.The two-level open system with only dissipation,and both dissipation and the normal electric field,are investigated.A proper mathematic transformation is used to eliminate the diagonal elements in the Hamiltonian and thus the odd self-to-self transitions.The same procedures are performed for a three-level system.Numerical results proves the consistency of pathway amplitudes by the new HE-OD method and Dyson integration.This research is in Chapter Four.