使用光學頻率梳精確測量其AC Stark效應

Abstract

由Hall等人在光學頻率梳的創新下，其尖光譜及免標記性，為高精度測量開啟了很多新的可能性。即便使用頻率梳，還是存在各種光譜不準確的來源，如壓力效應、塞曼效應、AC Stark位移和飛行時間展寬。而AC Stark位移引起理論興趣在於頻率梳與單脈衝的AC Stark位移情況並不相同。 近年來精確測量銫6S-8S的躍遷引起重大注意，原因在於這涉及到基礎物理定律如QED驗證、宇稱守恆及夸克質量變異。除此之外，此種躍遷有望成為新的光頻基準，導致新一代原子鐘。到目前為止，已有三篇關於高精度測量的論文被發表。它們彼此一致高達9位數，但也有小的差異達到100千赫。究其原因仍有爭議，但AC Stark位移被認為是可能的原因之一。 在此學位論文中，我們討論在雙光子躍遷中由頻率梳所誘發的AC Stark位移。首先我們解出與時相關的薛丁格方程式來模擬光譜實驗並計算AC Stark位移，再應用Floquet理論來驗證數值結果。以此可以發現AC Stark位移在使用頻率梳跟單脈衝的情況下，兩者有著顯著的差異。就我們的結果發現頻率梳所產生的位移量是單脈衝的4倍。已有很多篇論文，在頻率梳的實驗中採用單脈衝AC Stark位移數據來進行分析。而我們的研究顯示在計算AC Stark位移中頻率梳所影響的重要性。

The innovation of the optical frequency comb by Hall et al. has opened new possibilities in high precision measurement owing to the sharp spectral width and the marker free property. Even using an optical comb, however, there still exist various sources of inaccuracy in the spectrum, such as the pressure effect, the Zeeman effect, AC Stark shift, and time of flight broadening. Among the possible sources of uncertainty, the AC stark shift may attract theoretical interest, because the shift behavior is different from that in the case of single pulse. Recently precise measurement of cesium 6S-8S transition attracts significant attention since it is related to testing fundamental physics such as QED verification, the parity conservation, and quark mass variation. Besides these fundamental interests, this transition is expected as new optical frequency standard leading to next generation atomic clock. So far there have been three papers on high precision measurement reported. They agree with each other up to 9 digits, but there are small difference as large as 100 KHz. The reason for the discrepancies is still controversial, but the AC Stark shift is one of the possible reasons. In this thesis, we discuss the AC Stark shift in two-photon transition induced by an optical frequency comb. First we directly solve the time dependent Schrodinger equation to simulate the spectroscopy experiment and to calculate the AC Stark shift. After that we utilize the Floquet theory to reproduce the numerical results. The two calculations agree well with each other. We found that the AC Stark shifts by optical comb shows quite different behavior from that by a single pulse. In our case the shift by comb can be 4 times larger than that of the single pulse case. There have been many papers, in which the experimental results using the combs are analyzed using the data of single pulse AC Stark shift. Our study, however, indicate the importance of comb effect in calculating the AC Stark shift.