激子在量子微結構中之超輻射現象

Abstract

在本論文中，我們研究激子在不同量子微結構(量子阱、量子線、量子點及量子環)的超輻射衰變率及頻率遷移。同時，我們也考慮了不同維度間的過渡行為。在低密度的狀況下，我們忽略了激子的非玻色子對易關係。 這樣的狀況下，我們發現激子在量子阱(quantum wells)中的衰變率及頻率遷移，會隨阱寬的增加呈現震盪的行為，並且會慢慢從超輻射激子過渡成為三維的極化子(polaritons)。若考慮量子線(quantum wires)包夾在一平面共振腔，我們也發現當平面共振腔的距離等於半波長的整數倍時，激子的衰變率會明顯的加強；同時，其頻率遷移也會顯現出不連續的行為，這就是所謂的Purcell效應。為了可以量測到這個效應，我們考慮了一個簡單的模型：將一個兩能階的量子點(quantum dot)包夾在一平面共振腔內並且外加電極去測量電流。透過這樣的模型，也許可以直接由電性的量測去檢驗Purcell效應。此外，我們也發現，若將一量子環(quantum ring)放在平面共振腔內，也可以利用共振腔的物理特性去檢驗Aharonov-Bohm效應。

In this dissertation, we consider the superradiant decay rate and renormalized frequency shift of Wannier excitons in the quantum well, quantum wire, and quantum ring. The crossover behaviors from 3D to 2D, 2D to 1D, and 1D to 0D are also studied. The density of the excitons is assumed to be small so that one can neglect nonbosonic commutation relation of excitons. In semiconductor quantum wells, the superradiant decay rate and renormalized frequency shift are found to show oscillatory dependence on well widths. The crossover from the superradiant exciton to bulk polariton is also examined. In the case of quantum wires, it is shown that the dark-mode exciton can be verified experimentally when the wires are embedded in a planar microcavity. It is also found that the decay rate is greatly enhanced as the cavity length is equal to the multiple half-wavelengths of the emitted photon. Similar to its decay rate counterpart, the frequency shift also shows discontinuities at the resonant modes. Moreover, we have also considered the superradiant decay of a quantum ring Wannier exciton inside the planar microcavity. It is found the Aharonov-Bohm oscillations might be observable easily at some resonant peaks. On the other hand, we have also considered a quantum dot inside a microcavity. Instead of optical measurements, we point out that the Purcell effects can be verified electrically by measuring the current through a two-level quantum dot.