由於不同極性(polarization)的光遵循簡單的選擇律來激發出石墨烯裡的K跟K’的trion來得到可行的量子態轉換(quantum state transfer)並可應用在量子通訊的quantum repeater上。這篇論文主要研究光子(photon)跟共振腔裡的石墨烯山谷型位元(valley pair qubit)之間的量子態轉換。石墨烯山谷型位元是放在光子晶體共振腔上並置於微型共振腔裡面，使用兩個共振腔不僅可以增加光跟電子的交互作用還可以辨別量子態轉換裡進去跟出去的光。量子態的轉換主要有以下幾個過程:一開始光訊號依據不同的偏振(polarization)來帶有各種資訊，接著進入共振腔和石墨烯山谷型位元交互作用形成一種量子糾纏態(entangled photon-valley state)，再來量測從共振腔漏出的光的x方向或y方向的極性，進而把光的資訊轉移到石墨烯山谷型位元上。我們建立量子力學模型來描述量子態的轉換並得到yield和fidelity。Yield代表光子的成功率(偵測到的光子數/輸入訊號的光子數)，fidelity代表光子的保真率。最後我們用各種共振腔和位元的參數來得到yield和fidelity數值結果。

The optical excitation of graphene electrons is known to obey a simple selection rule in regard to the binary states of photonic circular polarization and electronic valley pseudospin, with the rule giving a close link - an approximate one-to-one correspondence - between the corresponding binary states. Thus, a highly faithful quantum state transfer (QST) can be implemented, at least in principle, between the polarization and the pseudospin, which could have important implications for quantum repeater protocol-based quantum communications. In this thesis, we perform a proof-of-principle study and investigate the QST between a photon qubit and a valley pair qubit - the system of two entangled valley pseudospins separately confined in coupled graphene quantum dots. For the demonstration, we consider the specific configuration where the valley qubit is placed inside both a micro-cavity and a photonic crystal cavity. The two cavities together provide i) enhancement of the electron-photon interaction and ii) differentiation between the incoming and outgoing light paths in the QST. The QST in the configuration proceeds in a series of steps. It starts with a) the arrival of a signal photon with quantum information already encoded in the polarization, followed by b) its entry into the micro-cavity and c) subsequent interaction with the valley qubit to form an entangled photon-valley state by the valley-polarization correspondence, and last, d) detection and measurement of the leaking photon from the photonic crystal cavity about its linear polarization. The last step d) projects out the photon component from entangled photon-valley state, thus leaving behind the quantum information in valley sector alone and completing the final transfer of quantum information between the two qubits. We set up a quantum mechanical description of the forgoing QST process and evaluate the corresponding yield and fidelity, which are defined, respectively, by (no. of detected photons) / (no. of signal photons) and |overlap between the transferred valley state and the signal state|2. Numerical work in our study shows promising results for the two forgoing figures of merits. Dependences of the yield and fidelity on various cavity and qubit parameters are also examined.

Content

Chapter1 Introduction 2
1.1 Motivation 2
1.2 This work 2
1.3 Valley Pair Qubits 3
1.4 Optical Matrix Element 5
1.5 Quantum State Transfer 8
1.6 Outline of the thesis 10

Chapter2 Theoretical Model 11

Chapter3 Result and Discussion 26

Appendix 34
Appendix A Time Reversal Symmetry 34
Appendix B Calculation 35

References 36

1.G. Y. Wu, N.-Y. Lue, and L. Chang, Phys. Rev. B 84, 195463 (2011)

2.G. Y. Wu, N.-Y. Lue, Phys. Rev. B 86, 045456 (2012)

3.Y. Rikitake, H. Imamura and H. Kosaka, Phys. Soc. Jpn (2007)