單一V型三能階原子在光子晶體中的自發輻射干涉現象

Abstract

原子在光子晶體中的自發輻射具有長時間記憶(long-time memory)的效應。 因此利用記憶核(memory kernel)我們可以了解原子在等向性(isotropic)及非等向性(anisotropic)光子晶體的自發輻射會導致碎形現象(fractal phenomenon)產生。 此種現象我們可以利用分數微積分(fractional calculus)來迅速地解決，而不用經過繁雜的複變函數積分來處理。此論文中，我們發現當調變單一V型三能階原子的躍遷頻率(transition frequency)和光能隙(photonic band-gap)時，激發態能階受量子干涉現象影響而產生的物理狀態可以分為四區：分別是反拘陷區(anti-trapping)、非居量反轉區(no population inversion)、增強居量區(enhanced population)和增強居量振盪區(enhanced periodic oscillation)。 除此之外，量子干涉現象亦使得光能隙在系統中產生高頻位移情況。藉由高頻位移的光能隙邊際，我們可以將單一多能階原子的物理狀態，簡單地以二能階原子來表達。

We study the spontaneous emission from a V-type three-level atom embedded in a photonic crystal with isotropic and anisotropic band structures. Through detuning the two allowed atomic transition frequencies with respect to the photonic band edge, we observed that the quantum interference between the two transitions and the coherent interference of the atom-field system lead to the splitting of the atomic energy levels into four regimes, namely anti-trapping, no population inversion, enhanced population, and enhanced periodic oscillation. The photon-atom bound states will not exist in the anti-trapping regime, but they do exist in the others. Furthermore, the V-type three-level atom system is equivalent to a two-level atom system for distinguishing the bound and unbound states if one up shifts the band edge of three-level atom system by two atom-field coupling constants.