利用串聯(lián)量子點晶體管測量固態(tài)量子比特

應用物理學論文編號:WLX093  字數(shù):11940,頁數(shù):30

目  錄
中文摘要……………………………………………………………………………………………  i
英文摘要……………………………………………………………………………………………  ii
目錄………………………………………………………………………………………………… iii
第一章     緒論…………………………………………………………………………………… 1
 1.1  量子計算簡介…………………………………………………………………………  1
 1.1.1 量子計算的發(fā)展………………………………………………………………  1
 1.1.2 量子計算的原理………………………………………………………………  1
 1.2  量子測量理論…………………………………………………………………………  2
       1.2.1 量子測量的觀點………………………………………………………………  2
       1.2.2.定性概述………………………………………………………………………  2
       1.2.3 定量簡介………………………………………………………………………  2
              1.2.3.1 可測量數(shù)據(jù)…………………………………………………………  2
              1.2.3.2 測量概率……………………………………………………………  3
 1.3  連續(xù)弱測量理論………………………………………………………………………  3
 1.4  量子點接觸（QPC）測量背景介紹…………………………………………………   4
       1.4.1 QPC測量背景…………………………………………………………………   4
       1.4.2 QPC測量原理…………………………………………………………………   4
第二章     Landauer-Büttiker方法簡介…………………………………………………………  6
 2.1   兩端器件介紹………………………………………………………………………   6
 2.2   電流算符……………………………………………………………………………   7
 2.3   平均電流……………………………………………………………………………   8
第三章     量子主方程方法……………………………………………………………………   9
 3.1   體系描述……………………………………………………………………………   9
 3.2   二階Born-Markov近似………………………………………………………………   9
 3.3   量子主方程…………………………………………………………………………  10
 3.4   與Landauer-Büttiker方法的比較………………………………………………  12
第四章     利用串聯(lián)量子點測量量子比特……………………………………………………  13
 4.1  系統(tǒng)簡介……………………………………………………………………………  13
 4.2  量子主方程…………………………………………………………………………  14
 4.3  約化動力學…………………………………………………………………………  15
  4.4  結果與討論…………………………………………………………………………  21
第五章     展望…………………………………………………………………………………  22
 5.1  能量重整化效應……………………………………………………………………  22
 5.2  測量時間與測量效率………………………………………………………………  23
第六章     結論…………………………………………………………………………………  24
致謝………………………………………………………………………………………………   25
參考文獻…………………………………………………………………………………………   26

摘     要
 
 本論文介紹了利用串聯(lián)量子點測量固態(tài)量子比特的方法。首先簡單介紹了當前量子輸運和測量領域所用的基本方法，即Landauer-Büttiker散射矩陣理論以及量子主方程方法。通過建立測量模型的哈密頓量，得到了約化體系的量子主方程。這一方程決定了約化體系狀態(tài)隨時間的演化。約化體系狀態(tài)有約化密度矩陣決定，其中包括對角元描述了量子態(tài)的概率，而非對角元則刻畫了量子態(tài)的相干。本論文采用數(shù)值模擬的辦法，演示了量子態(tài)（約化密度矩陣）隨時間的演化，并著重分析了退相干機制。其中發(fā)現(xiàn)，退相干強度與測量儀器中的隧穿耦合緊密相關，即隧穿耦合增強（減弱）時，量子比特的退相干就相應地增加（減少）。最后，簡要分析了能量重整化對量子測量的影響，并討論了如何有效的描述量子測量過程中的測量時間和測量效率問題。

關鍵詞：量子比特 量子測量 雙量子點 約化動力學
Abstract
 This thesis is dedicated to the problem of quantum measurement of a solid-state qubit by a serially coupled double-dot detector. Two basic approaches in quantum transport and quantum measurement are first introduced, i.e. the Landauer-Büttiker scattering theory and the quantum master equation approach. By establishing the Hamiltonian of the measurement setup, the master equation for the reduced system is derived. This equation determines the time evolution of the state of the reduced system. The reduced state of the system is characterized by the reduced density matrix, which includes the diagonal elements describing the probabilities, and off-diagonal elements depicting the coherence of the quantum states. In this thesis, by employing the numerical simulation method, the time evolution of the quantum state is demonstrated, with the focus on the analysis of the dephasing mechanism. It is found that the dephasing rate is closely related to the tunnel coupling in the measurement device. As the tunnel coupling enhances (reduces), the corresponding decoherence would increase (decrease). Finally, the effect of energy renormalization on the measurement is briefly analyzed, and the measurement time and measurement efficiency are discussed.
Keywords：qubit; quantum measurement; double quantum dots; reduced dynamics