在能量轉換的過程，已經被提出許多的方法，但是那麼多種方法，什麼時候應該使用什麼方法會比較好我們無從得知，在考慮不同的情況下，選擇適合的方法，讓以後的人在設計波導時能夠更加容易。首先，本論文介紹的第一種方法，主要是改良絕熱捷徑的分析，一般的絕熱系統下，要達到能量轉換必須得花很長時間，絕熱捷徑能夠將時間縮短，但卻會使得結果不夠穩定，因此我們使用的第一種方法主要是利用絕熱捷徑接近於絕熱系統，使得可以解決時間問題以及結果不穩定的狀況；第二種方法，主要是利用微擾理論探討，當我們已知有特定微擾下，可以直接將其優化，微擾理論在不同階數下精確度會不一樣，在此篇論文我們將討論到7階狀態。最終將此兩種方式的參數設計成相同型式，並且相互比較，判斷出在特定的情況下選擇較適合的優化方式。

The population transition have a lot of method be proposed. However, how should we choose the method in different situation we don’t know. In order to let design of waveguide easier, we want to select suitable methods under distinct circumstances. In this thesis, we will introduce two different methods, optimization of adiabaticity and robustness quantum control, respectively. The common shortcut to adiabaticity(STA) can improve long time problem of adiabatic transition, but the robustness is worse. And the first method not only can improve this problem but also can improve the robustness by approaching trajectory of adiabatic. The second method major is use the perturbation theory to improve particular perturbation. We compare distinct methods in the same parameters that we can know which method is better in different situation. Let the users can choose whichever particular method they want.

1. M. V. Berry, Histories of adiabatic quantum transitions. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 429, 61-62 (1990).
2. E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, Shortcuts to adiabaticity. Adv. At. Mol. Opt. Phys. 62, 117-169 (2013).
3. A. del Campo, Shortcuts to adiabaticity by counterdiabatic driving. Phys. Rev. Lett. 111, 100502 (2013).
4. B. T. Torosov, G. Della Valle, and S. Longhi, Non-Hermitian shortcut to adiabaticity. Phys. Rev. A 87, 052502 (2013).
5. David H. Mcintyre, Quantum Mechanics. Chapter 3 pp68~96
6. N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Laser-induced population transfer by adiabatic passage techniques. Annual Review of Physical Chemistry. 52(1): p. 763-809 (2001).
7. K. Bergmann, H. Theuer, and B. W. Shore, Coherent population transfer among quantum states of atoms and molecules. Reviews of Modern Physics. 70(3): p. 1003-1025(1998)
8. M. Born, and V. Fock, “Beweis des adiabatensatzes. Zeitschrift fu ̈r Phys. ” 51, 165-180 (1928).
9. H. R. Lewis Jr, and W. B. Riesenfeld, An exact quantum theory of the time‐dependent harmonic oscillator and of a charged particle in a time‐dependent electromagnetic field. J. Math. Phys. 10, 1458-1473 (1969).
10. C.-P. Ho, and S.-Y Tseng, Optimization of adiabaticity in coupled-waveguide devices using shortcuts to adiabaticity, Optics letters, 2015, 40, pp. 4831-4834
11. D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, Robust quantum control by a single-shot shaped pulse, Physical review letters, 2013, 111, pp. 050404
12. M. Ndong, G. Djotyan, A. Ruschhaupt, S. and Guérin, Robust coherent superposition of states by single-shot shaped pulse, Journal of Physics B: Atomic, Molecular and Optical Physics, 2015, 48, pp. 174007
13. A. Ruschhaupt, X. Chen, D. Alonso, and J. Muga, Optimally robust shortcuts to population inversion in two-level quantum systems, New Journal of Physics, 2012, 14, pp. 093040
14. S.-Y. Tseng, Robust coupled-waveguide devices using shortcuts to adiabaticity, Optics letters, 2014, 39, pp. 6600-6603
15. Y. Ma, P. Magill, T. Baehr-Jones, and M. Hochberg, Design and optimization of a novel silicon-on-insulator wavelength diplexer, Optics express, 2014, 22, pp. 21521-21528
16. S.-Y. Tseng, R.-D. Wen, Y.-F. Chiu, and X. Chen, Short and robust directional couplers designed by shortcuts to adiabaticity, Optics express, 2014, 22, pp. 18849-18859
17. A. Ruschhaupt, and J. Muga, Shortcuts to adiabaticity in two-level systems: control and optimization, Journal of Modern Optics, 2014, 61, pp. 828-832
18. X.-J. Lu, X. Chen, A. Ruschhaupt, D. Alonso, S. Guérin, and J. Muga, Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors, Physical Review A, 2013, 88, pp. 033406