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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 薛文証 | |
| dc.contributor.author | Chun-Ren Lin | en |
| dc.contributor.author | 林俊任 | zh_TW |
| dc.date.accessioned | 2021-06-08T00:25:13Z | - |
| dc.date.copyright | 2013-07-25 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-07-15 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/17611 | - |
| dc.description.abstract | 本論文主要的目的是研究在一維光晶格中的玻色-愛因斯坦凝聚特性。首先分別討論玻色-愛因斯坦凝聚以及光晶格，並說明研究將玻色-愛因斯坦凝聚置於光晶格的理由。接著，從平均場近似的Gross-Pitaevskii 方程式出發，並利用布洛赫理論，分別得到使用近似模型和解析模型的巨觀波函數的解。在近似模型中，顯示了不同光晶格位能與原子間非線性交互作用的影響。由系統中看到，當平均密度小於臨界原子密度時，能帶結構與一般情況並無明顯差別，而在平均密度大於臨界原子密度時，能帶結構會出現燕子尾巴和環的形狀，其為超流體之特性，此外，隨著原子平均密度越大，燕子尾巴和環的寬度也會隨之增大，即超流體特性更加明顯，再由流動密度得知，在布里淵區邊界，流動密度不再為零，其直接證實了超流體特性；最後利用解析模型求出對於位能為橢圓函數形式的穩態解，並用此穩態解觀察玻色-愛因斯坦凝聚的密度分佈以及相位分佈。 | zh_TW |
| dc.description.abstract | The main purpose of this thesis is to investigate the properties of Bose-Einstein condensates in one-dimensional optical lattice. First, the Bose-Einstein condensate and the optical lattice are discussed respectively. The reason why the Bose-Einstein condensates are placed in the optical lattice is also explained. With the Gross-Pitaevskii mean field approximation model and Bloch's theorem, the solution of macroscopic wave function for approximate model and analytical model can be obtained respectively. In the approximate model, the effect of the different optical lattice potentials and nonlinear interaction between atoms is shown. When the mean number density is smaller than critical number density, the band structure in this case is similar to that in the general case. However, when the mean number density is greater than critical number density, the swallowtails or loops emerge in the band structure. This represents the superfluidity. When the mean number density is increasing, the width of swallowtails and loops will increasing too. This means that the superfluidity is more apparent. Moreover, the current density is no longer zero in the Brillouin zone boundary, which confirms directly superfluidity. In addition, the stationary solution of the potentials as the elliptic function can be derived from the analytical model. According to the stationary solution, the density distribution and phase distribution of Bose-Einstein condensates can be observed. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T00:25:13Z (GMT). No. of bitstreams: 1 ntu-102-R00525077-1.pdf: 1297350 bytes, checksum: 7ef5bcf178a1500700b7041f7f18ef76 (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 摘要 i
Abstract ii 目錄 iii 圖目錄 v 表目錄 vii 符號表 viii 第一章 導論 1 1.1 背景與研究動機 1 1.2 歷史文獻回顧 3 1.3 論文架構 4 第二章 光晶格中的玻色-愛因斯坦凝聚 5 2.1 玻色-愛因斯坦凝聚 5 2.1.1 玻色-愛因斯坦凝聚理論 5 2.1.2 玻色-愛因斯坦凝聚的形成 6 2.2 光晶格 8 2.2.1 簡單一維光晶格 8 2.2.2 一般性且多維光晶格 13 2.3 在光晶格中的玻色-愛因斯坦凝聚 14 第三章 玻色-愛因斯坦凝聚之最低的布洛赫能帶結構 19 3.1 Gross-Pitaevskii 方程式 19 3.1.1 Gross-Pitaevskii 方程式的基本特性 19 3.1.2 在光晶格中的玻色-愛因斯坦凝聚之平均場模型 21 3.2近似模型 25 3.3非線性布洛赫能帶結構、化學位能及流動密度 27 3.3.1 原子間交互作用對能帶結構之影響 27 4.1解析模型 38 4.1.1 第一種穩態解 40 4.1.2 第二種穩態解 42 4.2波函數特性 47 4.2.1 密度分佈 47 4.2.2 相位分佈 50 第五章 結論與未來展望 69 5.1結論 69 5.2未來展望 71 參考文獻 72 | |
| dc.language.iso | zh-TW | |
| dc.title | 光晶格中的玻色-愛因斯坦凝聚特性 | zh_TW |
| dc.title | Properties of Bose-Einstein Condensates in Optical Lattices | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 洪姮娥,鄭勝文,溫新助,黃俊穎 | |
| dc.subject.keyword | 玻色-愛因斯坦凝聚,光晶格,超流體,能帶結構,波函數,密度分佈, | zh_TW |
| dc.subject.keyword | Bose-Einstein condensate,optical lattice,superfluidity,band structure,density distribution, | en |
| dc.relation.page | 76 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2013-07-15 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 工程科學及海洋工程學研究所 | zh_TW |
| 顯示於系所單位： | 工程科學及海洋工程學系 | |
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