Achieving Precise Quantum Control By Using Spin Echo Technique

Quantum Computation and Information are the most important research focuses in current physics. Quantum control is a coherent or non-coherent control of quantum systems which drive the system from any given initial state to any target state in limited time.Manipulation using magnetic field is a common method to control spin to an anticipated position. However, this process cannot keep the coherence of the spin in the evolution. Due to the environmental interaction, the spin will occur decoherence in the rotation process.Currently, most of the work we have done is to apply the p pulses to x or y axis, such that the spin recovers to its initial state.We first propose to use spin echo technique for quantum spin control to achievie precise quantum control. By choosing a suitable magnetic field direction and p pulse flip axis, we can drive the spin with spin echo to the final state that we expect with a very high degree of coherence. We show that the spin flip axis position is the bisector of the initial state and final state. Then we examine the relationship between the degree of coherence dependence and flip-axis position and the evolution of time. First we use the perturbation approach in the Hamiltonian of the quantum system for Winkler diagonalization. We found that the degree of quantum coherence is independent of position of flip axis. Then we calculate the degree of coherence with the non-perturbative quantum system and find the flip-axis position has no effect on the degree of coherence of quantum systems when the number of spin is large,whilebut in the small bath spin, the flip axis position influences the degree of coherence for specific values with no obvious rules. We use the exact diagonalization method for small bath and the CCE method for the large bath. We use CCE from perturbation system to non-perturbation system. This is the major innovation of this thesis.