| Since it was born, quantum control has already leaded to significant improvements in various technologies, such as magnetic resonance, prototype quantum computers, quan-tum high-precision sensors, quantum logic clocks, single atom transistors and so on. The 21st Century’s industrial revolution centres around quantum technology, and the society is looking forward to a bright prospect from it. Now, researchers are working on problems that obstruct the development of quantum control. Those problems include design, stabi-lization, error-correction, noise reduction and filtering, and combating decoherence and so on. The advancement of quantum control needs a coordination of divers areas, involving in mathematics, physics, control theory, dynamical systems, stochastic processes, signal processing and information science.In this paper, we respectively give control protocols for two non-degenerate N-dimensional quantum system with different energy level structures as well as their specific theoretical analysis. For the first quantum system, it has all equal energy gaps except the first one. While the another one has all distinct energy gaps. Considering their en-ergy structures fully, we proposed two simple and practical protocols. And the complete controllability of these protocols was proved with Lie algebra.In this paper, we used two kinds of external control fields to realize our proposals. One is harmonic fields, the other is square pulses fields. The evolution of the two systems controlled by these fields are analyzed theoretically. As a result, we deduce the analytic expresses that describe the relationship between control parameters and amplitudes of each energy eigen-state of the target state. With those relationship, we can determinate the control parameters through target states. Thus we finished our control protocols. Certainly, decoherence do not take into account in our protocols. Thus we expect further researches can keep on in the presence of environment. |
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