本論文致力於研究最佳化絕熱過程之理論分析與數值模擬。首先，我們介紹二能階系統的絕熱過程之基本理論，在一般的設計中，因為絕熱過程受限於絕熱態之間的耦合，絕熱態無法完全對應系統態的演化，亦即在沒有絕熱捷徑的情況下，絕熱過程難以達到完全轉換，我們首先透過Lewis-Riesenfeld不變量算符逆向操縱法計算絕熱捷徑，此捷徑擁有完全的轉換效率，但會降低絕熱過程中對於參數誤差的穩定性。因此我們透過量子力學分析系統態對應絕熱態的分量，設計出最佳化的絕熱捷徑，並藉由實際模擬的結果，驗證了最佳化的絕熱過程會保有完全轉換效率和對於參數誤差的穩定性。

This thesis is devoted to the theoretical investigation and numerical simulations of an optimal adiabatic transition aided by shortcuts to adiabaticity (STA). We begin by introducing the theory of adiabatic transition in two-level systems. In general design, adiabatic states cannot correspond to system states evolution which is perturbed by the coupling of adiabatic states. In other words, adiabatic transition is hard to achieve complete population transfer without shortcut design. The Lewis-Riesenfeld invariant engineering protocol is introduced into adiabatic transition to calculate the STA. These shortcuts will lead to complete population transfer but lose the robustness which is the advantage of adiabatic transition. Hence we propose the optimal adiabatic transition designed by analyzing the fraction of system states projected on adiabatic states with quantum mechanics. The results from simulations support our theory very well. We show that the optimal adiabatic transition combines the advantage of complete population transfer and robustness.

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