近來李黃楊(Lee-Huang-Yang)量子修正在冷原子系統激起了很高的研究興趣。在長程序電偶極(long-ranged dipolar)系統中，李黃楊修正可以導致穩定的超固態(supersolid state)，而在相互吸引的的二分量短程序(two-component short-ranged)系統中，李黃楊修正可以導致量子液滴(quantum droplet)的形成。
在本論文中，我研究李黃楊修正如何影響兩個膨脹的玻色-愛因斯坦凝聚體(Bose-Einstein condensates)的干涉(interference)。從具有李黃楊修正的三維Gross-Pitaevskii (GP)方程理論開始，首先推導出相關的準一維二分量耦合方程式，藉以研究兩個相干(coherent)、空間分離的凝聚體的干涉。接著，數值求解耦合方程式得到兩個膨脹冷凝物的干涉結果。透過控制變因，一次只改變一個參數，我具體得出干涉波長如何受到李黃楊修正的效應的影響。我們的研究結果應對相關實驗具參考價值。

Recently Lee-Huang-Yang (LHY) correction has stimulated a lot of interest in ultracold atoms. In long-ranged dipolar systems, LHY correction can result in stable supersolid states, whereas in a two-component short-ranged system with attractive interspecies interaction, it could lead to a novel state of quantum droplets. In this thesis, I investigate the effect of LHY correction on the interference of two expanding Bose-Einstein condensates. Starting from a general three-dimensional theory of Gross–Pitaevskii equation with the LHY correction, I derive the coupled equations for the wave functions of two
coherent, spatially displaced condensates in a quasi-one-dimensional geometry. Solving the coupled equations enables the study of interference of the two expanding condensates along a particular direction. By varying the parameter one at a time, our simulations show explicitly how the wavelength of the interference depends on the effect of LHY correction. Our results should shed some light on the relevant experiments.

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