電子自旋糾纏與量子點的近似互換對稱性

The Approximate Exchange Symmetries in the Quantum Dot Spin-entangler with Anderson Hamiltonian and on-site Coulomb Interaction

解雯娟(WEN-CHUAN HSIEH)

指導教授 ： 周志隆

中原大學/理學院/應用物理研究所/碩士(2008年)

https://doi.org/10.6840/cycu200900586

摘要

在本篇論文中，我們所要討論的是電子自旋糾纏。糾纏態可以藉
由雙電子經過量子點來產生。此量子點模型有一個輸入端與兩個輸出
端，而且這個量子點本身具有某些交換對稱性。在此只針對transition
amplitude 做討論，且只考慮transition amplitude 的最低階項。除了按
部就班地計算出所有結果外，也可以利用量子點模型的對稱性來簡略
計算。無論量子點內有多少能階，所有transition amplitudes 的結果都
與庫倫交互作用有關。結果中所有特殊因子都可以用量子點的對稱性
來說明，例如像庫倫交互作用這樣特殊的因子。因為在考慮transition
amplitudes 的多階項後此對稱性將不再存在，所以此對稱是近似互換
的對稱。

關鍵字

電子自旋 ； 量子點

並列摘要

In this thesis we re-investigate the electron spin-entangler that consists
of a single-level quantum dot, an input lead and two output leads. We find
that there are two exchange symmetries among the two-electron transition
amplitudes in the lowest order of calculation O(V4). Via the exchange
transformations all the virtual tunneling paths that contributes to the
transition amplitudes can be obtained a small set of virtual paths called
the inequivalent virtual paths in the thesis. We show that all the transition
amplitudes can be calculated by considering only the inequivalent paths.
We also find that all the fully suppressed transition amplitudes in O(V4)
are odd-symmetric under both the exchange transformations. The
exchange symmetry does not exist in higher orders of calculation.

並列關鍵字

Quantum Dot

參考文獻

[1] H. Bennett and J. Wiesner, Physical Review Letters 69, 2881 - 2884

[4] J. J. Sakurai, Modern Quantum Mechanics (revised edition, 1994) p.262.

[5] Guido Burkard, Journal Physics: Condensed Matter 19 (2007) 233202.

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