臺灣博碩士論文加值系統

最近由McClure 等人在實驗上量測出兩個平行耦合的量子點在 Coulomb blockade regime 下的cross correlation。他們發現cross noise spectrum 形成一個四葉的圖案而且可以藉由外在的gate voltage 和偏壓來調控此cross correlation。此外， Sukhorukov 等人也量測量子點與quantum point contact 該耦合系統中電子傳輸的條件式統計分布。所謂的條件式統計指的即為給定系統中某一電流的量測結果，則系統其他電流隨此量測結果的統計分佈。電流的條件式統計分布完全異於其平均電流。在此論文中，藉由the number-resolved quantum master equation approach 與the full counting statistics method，我們計算在此兩系統中電子傳輸的條件式統計，並且在雙耦合量子點系統中討論此cross noise spectrum 四葉圖案其隱含的物理圖像。條件式統計比純粹的平均量更有助於我們瞭解該系統的性質。

Recently measurements of the cross correlation between current fluctuations in two capacitively coupled quantum dots in parallel in the Coulomb blockade regime have been reported
by McClure et al. They …find the cross noise spectrum forms a quadrupole pattern that is tunable by external gate voltage and source-drain bias voltage. In addition, conditional statistics of electron transport in nanoscale conductors has also been measured with a quantum dot coupling to a quantum point contact in experiment by Sukhorukov et al. The conditional counting statistics that is the statistical current fluctuations of one system given the observation of a particular current in the other system could be substantially different from their unconditional counterpart. In this thesis, based on the number-resolved quantum master equation approach and the full counting statistics method, we evaluate the conditional statistics of current cumulants in both systems and discuss the underlying dynamics corresponding to different regimes in the quadrupole pattern of the two-coupled quantum dot system. We …find the conditional statistics can help better understand the system’''s properties as it provides more information than the usual unconditional statistical quantities.

List of Figures iii
1 Introduction 1

2 Theoretical methods 7
2.1 Quantum master equation for quantum transport 7
2.1.1 Stochastic description of the system-bath interaction 7
2.1.2 Quantum master equation approach to quantum transport 9
2.2 Full counting statistics 13
2.2.1 Basic concepts 13
2.2.2 The FCS in the master equation 16

3 Conditional statistics (I) A quantum dot measured by a quantum point contact 21
3.1 Model Hamiltonian 21
3.2 Unconditional and conditional dynamics 24
3.3 Unconditional and conditional statistics 30

4 Conditional statistics (II) Two coupled quantum dots 44
4.1 Model Hamiltonian 44
4.2 Unconditional and conditional statistics 47
4.2.1 Cross correlation noise at different gate voltages 47
4.2.2 Probability distribution and counting statistics of electron transport 50

5 Conclusion 84
Bibliography 86

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