幾何相位和電子自旋軌道交互作用

Abstract

在使用活動式量子位元的計算模式下，我們分別報告兩個能對實現量子計算有用的研究。在這份報告的第一個部分，我們在理論上探討了半導體對稱雙能障結構中的自旋相依穿隧效應。我們的計算是基於等效的單個能帶的Hamiltonian以及Dresselhaus 自旋軌道耦合項。我們展示，帶有不同自旋方向的電子，彼此穿隧時間的比例變化可達幾個數量級。而這大且可調整的穿隧時間比例，可以作為發展全半導體的動態spin filter 的基礎。 在這份報告的第二個部分，我們提出一種進行量子計算的架構，使用ballisticelectron 作為量子位元，以及耦合的量子環作為量子邏輯閘。在這個架構中，兩條相鄰且一維的量子線形成一個量子位元，它們被接到兩個互相耦合的量子環。而量子環圈繞住的奈米磁鐵提供所需的磁通量。在Aharonov-Bohm 效應下，我們仔細設計電子波函數受到的相位調變，以促成可重新程式化且可動態控制的量子邏輯閘。基於這個架構我們可製造一組有高fidelity 的量子邏輯閘。

We present two separate research which, under the computing scheme with mobile qubits, could be useful to the implementation of quantum computation. In the first part of this report, spin dependent tunneling in semiconductor symmetric double barrier structures is studied theoretically. Our calculation is based on the effective one band Hamiltonian and Dresselhaus spin-orbit coupling. We demonstrate that the ratio of the tunneling times of electrons with opposite spin orientations can vary over a few orders in magnitude. The large and tunable ratio of the tunneling times can serve as the basis in development of all-semiconductor dynamic spin filters. In the second part of this report, we propose an architecture to perform quantum computation, using ballistic electrons as qubits and coupled quantum rings as quantum gates. In the proposed architecture two adjacent one-dimensional wires, creating a single qubit, are connected to two coupled quantum rings, where the required magnetic flux is provided by enclosed nano-sized magnets. The phase modulation of the wave function of the ballistic electrons under the Aharonov-Bohm effect is carefully designed to facilitate re-programmable and dynamically controllable quantum gates. A set of quantum gates with high fidelity can be constructed on the basis of this architecture.