以量子協同態探討原子團散射之協同蘭姆位移

Abstract

由於原子間具有偶極-偶極交互作用，原子團展現出有別於單原子系統的協同現象，其中一個重要的物理量為協同蘭姆位移。近年來，協同蘭姆位移已於原子團散射光譜中被觀測到，然而在不同幾何形狀的系統中其尺度參數並不相同，並且此頻率位移尚欠缺理論詮釋。我們利用數值模擬計算了典型的高密度冷原子團散射光譜，發現其具有數個峰值(頻移)。透過分析原子團的量子協同態，我們將這些峰值區分為兩種不同物理來源。其一來自於原子團整體的高激發量，這類頻移相當微小，並且與各系統參數皆無明顯相關；另一來自於特定協同態的激發，這些協同態的空間頻率與輻射場相當接近，因此能產生較強的散射光，這類頻移與原子團的光學深度成正比。我們的研究提供了協同蘭姆位移的理論詮釋，並解釋了不同實驗系統中所呈現的不同尺度參數。

The cooperative Lamb shift is an important physical quantity that reveals the cooperative nature of an atomic ensemble in light-matter interaction. In particular, many efforts have been made to investigate the cooperative Lamb shift identified from the forward scattering spectrum, both theoretically and experimentally. However, the physical interpretation of the cooperative Lamb shift has not been clarified. The scaling of the shift even differs in different kinds of ensembles. In our work, we investigate cold, dense atomic ensembles interacting with a plane-wave laser field in the low-excitation regime. The ensemble is described by a non-Hermitian effective Hamiltonian which contains the dipole-dipole interaction between every pair of atoms. We numerically compute the forward scattering spectrum and find several peaks (shifts). We demonstrate that by an appropriate choice of collective basis, the physical interpretations of the shifts are clearly revealed. We thus distinguish two kinds of shifts. One results from the large excitation of the ensemble, and the shift is relatively small regardless of the parameters. The other is due to the large correlation between atoms and the resulting strong coherent scattering, when the laser is tuned resonant with the collective states whose spatial frequencies are closest to the field. We find that the latter kind of shifts increases linearly with the optical depth of the ensemble but the former does not. Our analysis not only gives intuitive interpretation of the cooperative Lamb shift, but also explains why there seems to be different scalings in different studies, since there are actually two kinds of shifts.