Reduction Of Dimensions Of Quantum Multi-level Systems Controlled By Lasers

Quantum theory has changed the landscape of human society since it was found in the 20th century. It established the foundation for understanding and explaining phenomena in atomic and sub-atomic scale, and promoted the development of laser, semi-conductor, nuclear power and so on. During its development, Quantum theory is fusing with other branches of science. Quantum control is a new area of science born from the combination of quantum theory and control theory. It may bring in revolution to computer science, medical and life science. The application of quantum control in chemical reaction has already produced exciting achievements and the invention of laser, and further accelerated the development of the theory of quantum coherent control.This thesis discusses how the dimension of a multi-level quantum system is reduced to a simple system when it is controlled by a short laser pulse. We consider the effect of near degenerate eigenstates, and the strength of the laser. The objective is to control the collective population on all excited states. We treat the system with Rotating Wave Approximation (RWA) and perturbative theory. Precise and approximate model of pulse-driven two-level systems are studied and compared with the original multi-level systems. The population transfer of multi-level quantum system controlled by short pulsed is analyzed in different situation.In the thesis, we focus on the multi-level quantum system with near degenerate eigenstates, and discuss the population transfer from the ground state to the near-degenerate excited states. It is noted that in the case of both weak and strong field, the multi-level system can both be reduced to a two-level system. The results could be generalized to a multi-level system with several sets of near-degenerated eigenstates. The conclusion could be utilized to identify the effective dimension of a quantum multi-level system controlled by laser.