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研究生:陳俊諭
研究生(外文):Chen, Jun-Yu
論文名稱:長程序交互作用玻色原子團的能隙孤粒子
論文名稱(外文):Gap Solitons in an Ultracold Bose Gas with Long-Range Interaction
指導教授:吳文欽吳文欽引用關係
指導教授(外文):Wu, Wen-Chin
學位類別:碩士
校院名稱:國立臺灣師範大學
系所名稱:物理學系
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:中文
論文頁數:54
中文關鍵詞:玻色-愛因斯坦凝聚雷德堡綴飾原子超固態能隙孤粒子
外文關鍵詞:Bose-Einstein condensationRydberg-dressed atomssupersolidgap solitons
相關次數:
  • 被引用被引用:0
  • 點閱點閱:153
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  • 下載下載:6
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本論文研究雷德堡綴飾玻色原子團 (Rydberg-dressed atoms)置放入一維光晶格 (optical lattice) 中,在原子長距離交互作用半徑 (blocade radius) $ r_{c} $ 和單位晶格長度(lattice constant) $ d $這兩種距離尺度競爭下,可能得到分數型(fractionally modulated supersolid state)分布的超固態和對應的基本能隙孤粒子(fundamental gap solitons)。研究發現這個長程序作用力系統具有短程序作用力系統很不同的孤粒子行為,例如:多變分數型態的波型及具有可能的量子震盪行為。
Ch1 Introduction 1
1.1 Gross–Pitaevskii equation 2
1.2 Elementary excitaions 3
1.3 BEC in periodic potentials 7
1.4 Solitons 8
1.5 BEC with long-range interaction 10

Ch2 Rydberg-dressed Systems 12
2.1 Dressed atoms 13
2.2 Rydberg-dressed atoms 14
2.3 Superfluid and roton instability 17
2.4 Rydberg-dressed atoms in periodic potentials 20

Ch3 Gap Solitons in Rydberg-dressed Systems 23
3.1 Numerical approach to gap solitons 24
3.2 Gap solitons with short-range interaction 27
3.3 Gap solitons with long-range interaction 31

Ch4 Dynamics and Stability 39
4.1 Evolution and stability 40
4.2 Quantum oscillation 45
4.3 Stationary vs. oscillation 49

Ch5 Conclusion 50

Bibliography 52

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[12] C.-H. Hsueh, T.-C. Lin, T.-L. Horng, and W. C. Wu. Quantum crystals in a trapped rydberg-dressed bose-einstein condensate. Phys. Rev. A, 86(013619), 2012.

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[17] A. J. Leggett. Can a solid be ”superfluid”? Phys. Rev. Lett., 25(1543), 1970.

[18] Nigel R. Cooper and Zoran Hadzibabic. Measuring the superfluid frac-tion of an ultracold atomic gas. Phys. Rev. Lett., 104(030401), 2010.

[19] L.P. Pitaevskii. Nonlinear Waves: Classical and Quantum Aspects. Springer Netherlands, 2005. p175-p192.

[20] C.H. Hsueh, Y.C. Tsai and W.C. Wu. Intrinsic-to-extrinsic supersolid transition and fractionally modulated states in a lattice ultracold bose gas with long-range interaction. Phys. Rev. A, 92(013634), 2015.

[21] T.F. Xu, X.M. Guo, X.L. Jing, W.C. Wu, and C.S. Liu. Gap solitons and bloch waves of interacting bosons in one-dimensional optical lat-tices: From the weak- to the strong-interaction limits. Phys. Rev. A, 83(043610), 2011.

[22] Mordechai Segev Zhigang Chen and Demetrios N Christodoulides. Opti-cal spatial solitons: historical overview and recent advances. Phys. Rev. A, 75(086401), 2012.

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[24] Pearl J. Y. Louis, Elena A. Ostrovskaya, Craig M. Savage, and Yuri S. Kivshar. Bose-einstein condensates in optical lattices: Band-gap struc-ture and solitons. Phys. Rev. A, 67(013602), 2003.

[25] T. Mayteevarunyoo and B. A. Malomed. Stability limits for gap soli-tons in a bose-einstein condensate trapped in a time-modulated optical lattice. Phys. Rev. A, 74(033616), 2006.

[26] Yongping Zhang and Biao Wu. Composition relation between gap soli-tons and bloch waves in nonlinear periodic systems. Phys. Rev. Lett., 102(093905), 2009.

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[29] Andrey A. Sukhorukov and Yuri S. Kivshar. Nonlinear localized waves in a periodic medium. Phys. Rev. Lett., 87(083901), 2001.

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[31] J. J. Sakurai and Jim J. Napolitano. Modern Quantum Mechanics. Addison-Wesley, 2nd edition, 2010. (Ch4-2 and Problems 6).

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