量子光學中的表面電漿子問題

Abstract

在本論文中，我們首先計算二能階單量子點激子耦合到量子線上的表面電漿子之衰變率，我們發現該衰變率因為其與表面電漿子的耦合非常強而被大大的提升。在色散曲線的相對極小值附近，衰變率甚至會被提昇至無窮大，這告訴我們在這一範圍內使用馬可夫近似是不恰當的，於是我們借用了在光子晶體中能隙附近的處理方式，以非馬可夫來重新計算量子點激子的衰變率之時間演化，並得到相對應的振盪行為。我們並提出藉由量子線上的表面電漿子的散射來達到雙量子點的糾纏態的想法，實際運算後發現，假使我們在量子線的兩端並沒有偵測到表面電漿子的訊號，這表示雙量子點的糾纏態已經產生。為了避免表面電漿子在傳播中耗散，我們提出使用兩個同時耦合到完美波導的小量子線來取代原有的長量子線，並介紹了Lindblad形式的master方程來涵蓋耗散的效應且進一步計算concurrence的時間演化。

In this thesis, we examine the spontaneous emission of a two-level emitter, quantum dot exciton, into surface plasmons propagating on the surface of a cylindrical nanowire. The numerically obtained dispersion relations are found to strongly influence the spontaneous emission rate. At certain values of the exciton bandgap, the emission rates can go to infinity due to the band-edge feature of the dispersion relations. Borrowing the idea from the photonic crystals, we model the quantum-dot exciton dynamics with a non-Markovian way and demonstrate that the decay can undergo an oscillatory behavior. In addition, we theoretically study coherent single surface-plasmon transport in a nanowire strongly coupled to two quantum dots. Using a real-space Hamiltonian we find analytical expressions for the transmission and reflection coefficients and dot-dot entanglement. Our results show that remotely entangled states can be created if there is no out-going surface plasmons detected at both ends of the wire. We further use two small wires evanescently coupled to a dielectric waveguide instead of a long wire to minimize the dissipations during propagation, and introduce the Lindblad form master equation to include the dissipations and calculate the concurrence dynamics.