在矽中被驅動的單一磷供體之自旋在連續測量下的動力行為

在本論文中，我們研究如何透過連續弱測量(continuous weak measurement)來分辨量子系統的狀態。我們的系統是由一個在矽中的單磷原子之核自旋(nuclear spin)耦合電子自旋來組成，而且磷原子上的電子還隧道耦合一個被電荷感應靈敏的量子點接觸(quantum point contact)所量測之電子地點。在當電子的基曼能量分裂遠大於超精細交互作用時，磷原子的自旋可以近似成一個以z分量自旋極化為特徵基底的簡單四能階系統，藉著施加電子自旋共振(electron spin resonance)將電子從低能階激發到高能階，讓電子之後可以非相干性穿隧到和系統耦合的電子地點而使量子點接觸的電流產生變化，除此之外我們還施加核磁共振(nuclear magnetic resonance)去改變核自旋的狀態。我們使用非條件主方程和條件主方程來描述這個連續量子測量過程的動力行為，也計算通過量子點接觸的傳輸電流和對電流-電流的時間關聯函數(current-current two-time correlation functions)進行傅立葉轉換後得到的量子點接觸電流噪聲頻譜(current noise spectrum)，然後我們就研究在條件動力行為下電流是如何隨著核自旋狀態做變化，而這個測量方法將會和在半導體中首次對單一核自旋進行連續弱測量的實現息息相關。

關鍵字

量子點接觸；核自旋；電子自旋共振；核磁共振；時間關聯函數；電流噪聲頻譜；連續弱測量

並列摘要

In this thesis, we investigate how to distinguish the state of a quantum system under continuous weak measurements. Our system is composed of a nuclear spin coupled to an electron spin in a single phosphorus atom in silicon. Moreover, the electron in the phosphorus atom is tunnel-coupled to an electronic site which is subject to a measurement by a charge-sensitive detector of a quantum point contact (QPC). In the case when the electron Zeeman energy splitting is much larger than the hyperfine interaction, the spins in a phosphorus atom can be approximated to a simple four-level system with z-component spin polarizations as eigen basis states. By performing electron spin resonance (ESR) on the electron to excite it to the higher level, the electron then can tunnel incoherently to the electronic site coupled to the system, causing change in the QPC current. Furthermore, we perform nuclear magnetic resonance (NMR) to vary the state of the nuclear spin. We describe the dynamics of the continuous quantum measurement process using the unconditional and conditional master equations. We also calculate the transport current through the QPC, and the QPC current noise spectrum after performing the Fourier transform on the current-current two-time correlation functions. Then, we investigate how the current changes with the state of the nuclear spin in the conditional dynamics. This measurement scheme will be relevant to the implementation of the first continuous weak measurement of a single nuclear spin in a semiconductor.

並列關鍵字

quantum point contact ； nuclear spin ； electron spin resonance ； nuclear magnetic resonance ； two-time correlation functions ； current noise spectrum ； continuous weak measurement