對於量子力學而言，對稱假說(symmetrization postulate)為描述有多個等同粒子(identical particles)的系統時最基本的準則。而這些等同粒子的行為也必須遵守由對稱假說所衍生出來的統計規則，如費米-狄拉克統計(Fermi-Dirac statistics)與玻色-愛因斯坦統計(Bose-Einstein statistics)。然而在廣義場論(generalized field theory)的研究裡，卻發現系統有違反對稱假說的可能性。到目前為止，不僅違反對稱假說的理論尚未建立完備，同時，違反對稱假說的可能性也沒有實驗上的證明。

本論文以研究二氧化碳分子在4.3 μm (0001-0000)附近的吸收來驗證對稱假說。以結合摻銣釔鋁石榴石雷射(Nd:YAG, 1 W, 1064 nm)以及鈦藍寶石雷射(Ti:Sapphire, 1.8W, 780~870 nm)經過週期極化反轉鈮酸鋰(PPLN：Periodically Poled LiNbO3)晶體後產生的差頻(DFG：Difference Frequency Generation)雷射作為研究光源，同時藉由FM (Frequency Modulation)飽和吸收光譜的機制，將鈦藍寶石雷射鎖在碘分子的超精細結構上以降低此中紅外光的頻率不準度。利用此光源以及吸收長度為100公尺的multi-pass cell在對稱假說所不允許的躍遷位置((0001-0000) R(25), 2367.266430 cm-1)掃頻，並且選取(0221-0220) R(80)為marker line (2367.229989 cm-1)，同時利用週期平均法(cyclic average method)來消去伴隨multi-pass cell而來的干涉條紋。

到目前為止，利用本系統可將二氧化碳分子中兩個O16間forbidden exchange-antisymmetric states的上限推至 ，此結果比現有文獻中上限的極值 小兩個數量級。期望在不久的將來可以將上限再推至更小的極限以幫助量子理論的發展。

The symmetrization postulate (SP) is regarded as the foundation of quantum mechanics. It stated that wavefunction of bosons must be symmetry, and fermions' must be anti-symmetry with respect to exchange of two identical particles. Recently, there were some theories predicted the possible violation of symmetrization postulate. In order to verify these predictions, the existence of the absorption lines forbidden by the SP is searched by high sensitive spectroscopic method.

We use a tunable single-frequency mid-infrared PPLN (periodically poled lithium niobate) DFG (Difference Frequency Generation) source and a multi-pass absorption cell to search the forbidden exchange-antisymmetric line 0001-0000 R(25) of carbon dioxide spectrum. The DFG source is pumped by a single frequency Nd:YAG laser (1 W, 1064 nm) and a single frequency Ti:Sapphire laser (1.8 W, 780~870 nm). The Ti:Sapphire laser is frequency locked on the hyperfine structure of iodine molecule to reduce the frequency drift of the DFG source. We determine the upper limit of symmetry-violation parameter with a nearby SP allowed weak absorption line 0221-0220 R(80). For the purpose of increasing the sensitivity, we use cyclic average method to eliminate the fringe due to the optical interference of the multi-pass absorption cell. Furthermore, we average the results of 688 scans to reduce the noise.

We have pushed the upper limit of symmetry-violation parameter to . To our knowledge, our result was two order lower than previous works. In the future, we will further improve the upper limit by reduce the drift of DFG source. This research is important for the fundamental of quantum mechanics.

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