本篇論文中介紹了在電磁誘發透明現象與撥色愛因斯坦凝聚體在非零溫時的性質與動力學行為。
我們發展了一套數值方法處理考慮原子運動後的電磁誘發透明介質。而在玻色凝聚體方面，我們應用了
隨機投射的Gross-Pitaevskii方程式來研究多分量凝聚體在非平衡過程下的動力學行為。

電磁誘發透明系統的討論包含在論文的第一章到第五章針。我們詳細的寫下如何處理非零溫的電磁誘發透明系統。首先我們利用薛丁格方程式在伽利略變換下的不變性成功的將寫下包含原子運動後描述電磁誘發透明系統的方程組。接著我們推導出一組與溫度有關的等效參數來描述此系統在非零溫的定量性質。最後，我們將上述的數值方法應用到靜止光脈衝系統上,並討論如何在冷原子介質中產生靜止光脈衝。

非零溫的玻色凝聚體的部分位於論文本文中的第六章到第十章。我們首先介紹描述玻色氣體在非零溫時動力學行為的隨機投射Gross-Pitaevskii方程式。接著我們將其應用到多分量的自旋玻色氣體，並研究在旋轉凝聚體與考慮自旋軌道耦合作用的旋量凝聚體中拓樸缺陷的形成過程。最後，我們在線性耦合的玻色凝聚體中探討降溫過程中形成的缺陷是否遵守Kibble-Zurek機制所預測的行為。我們發現由拓樸保護的約瑟芬渦流在降溫速度快時其數目符合Kibble-Zurek的預測，然而在降溫速度較慢時其數目則少於Kibble-Zurek 所預測的數目。最後我們也分析了與Kibble-Zurek的預測發生分歧的原因。

This thesis reports the theoretical progress of the properties and dynamics of electromagnetically induced transparency (EIT) and Bose-Einstein condensate. We develop a numerical scheme to include the atomic motions in the EIT medium and we apply the stochastic projected Gross-Pitaevskii equation to study the non-equilibrium dynamics in multi-component Bose condensates.
In the part of EIT at non-zero temperature, by using the invariance of the Schr\"{o}dinger equation under the Galilean transformation, we successively include the atomic random motion in the EIT calculation and the numerical results agree favorably with the experimental data. We also derive a set of effective parameters which are temperature dependent. This provides the understanding how the atomic motion affect the EIT medium quantitatively. Finally, we apply the aforementioned numerical method to the stationary light pulses (SLPs) based on the effect of EIT with counterpropagating laser fields and show how a SLP form in cold media.
In the part of non-zero temperature BEC, we briefly discuss the properties of the stochastic projected Gross-Pitaevskii equation (SPGPE) for the Bose gases at non-zero temperature. Apply the SPGPE to spinor Bose condensate, we study the formation of the topological defects in rotating spin-1 Bose gas and spin-orbit coupled spin-1 Bose gas. Finally, we test the Kibble-Zurek scaling for the topological protected Josephson vortices in a linearly coupled Bose condensate. Our simulations reveal a -1/4 power-law scaling of defect number with quench time for fast quenches,consistent with the Kibble-Zurek mechanism. However, slow quenches show stronger quench-time dependence
that is explained by the stability properties of Josephson vortices, revealing the boundary of the Kibble-Zurek regime.

[1] Claude Cohen-Tannoudji and David Guery-Odelin, ADAVANCES
IN ATOMIC PHYSICS (World Scientic Singapore, 2011).
[2] D. D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk,
Phys. Rev. Lett. 83, 1767 (1999).
[3] K.-J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 66,
2593 (1991).
[4] J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67, 3062
(1991).
[5] L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature
(London) 397, 594 (1999).
[6] H. Schmidt and A. Imamoglu, Opt. Lett. 21, 1936 (1996).
[7] D. M. Stamper-Kurn et al., Phys. Rev. Lett. 80, 2027 (1998).
[8] Y.-H. Chen et al., Phys. Rev. Lett. 108, 173603 (2012).
[9] Y.-H. Chen et al., Phys. Rev. Lett. 110, 083601 (2013).
[10] B. Zhao, Y.-A. Chen, X.-H. Bao, T. Strassel, C.-S. Chuu, X.-M.
Jin, J. Schmiedmayer, Z.-S. Yuan, S. Chen and J.-W. Pan, Nature
Phys. 5, 95 (1995).
[11] M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and
E.A. Cornell, Science 269, 198 (1998).
[12] C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, Phys.
Rev. Lett. 75, 1687 (1995).
[13] K. B. Davis, M. -O. Mewes, M. R. Andrews, N. J. van Druten, D.
S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969
(1995).
[14] Tin-Lun Ho, Phys. Rev. Lett. 81, 742 (1998).
[15] T. Ohmi and K. Machida, J. Phys. Soc. Jpn. 67, 1822 (1998).
[16] Yuki Kawaguchi and Masahito Ueda, Physics Reports 520, 253-381
(2012).
[17] P. B. Blakie, A. S. Bradley, M. J. Davis, R. J. Ballagh, and C. W.
Gardiner, Adv. Phys. 57, 363 (2008).
[18] C. N. Weiler et. al., Nature 455, 948 (2008).
[19] A. S. Bradley, C. W. Gardiner, and M. J. Davis 77, 033616 (2008).
[20] S. W. Su, C. H. HsueH, I. K. Liu, Y. C. Tsai, T. L. Horng, S. C.
Gou, and W. M. Liu, Phys. Rev. A 84, 023601 (2011).
[21] S. W. Su, I. K. Liu, Y. C. Tsai, W. M. Liu, andS. C. Gou, Phys.
Rev. A 86, 023601 (2012).
[22] Shih-Wei Su, Shih-Chuan Gou, Ashton Bradley, Oleksandr Fialko,
and Joachim Brand, Phys. Rev. Lett. 110, 215302 (2013).
[23] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod.
Phys. 77, 633 (2005), and references therein.
[24] S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[25] J. E. Field, K. H. Hahn, and S. E. Harris, Phys. Rev. Lett. 67,
3062 (1991).
[26] M. Fleishhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[27] C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature (London)
409, 490 (2001).
[28] M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R.
Weich, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully,
Phys. Rev. Lett. 82, 5229 (1999).
[29] A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev.
A 66, 013805 (2002).
[30] D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M.
D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[31] O. Kocharovskaya, U. Rostovtsev, and M. O. Scully, Phys. Rev.
Lett. 86, 628 (2001).
[32] A. V. Turukhin, V. S. Sudarhanam, M. S. Shariar, J. A. Musser,
B. S. Ham, and P. R. Hemmer, Phys. Rev. Lett. 88, 02362 (2001).
[33] Y. W. Lin, W. T. Liao, T. Peters, H. C. Chou, J. S. Wang, H. W.
Cho, P. C. Kuan and I. A. Yu, Phys. Rev. Lett. 102, 213601 (2009).
[34] L.-M. Duan, J. I. Cirac, and P. Zoller, Science 292, 1695 (2001).
[35] T. Chaneliere, D. N. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A.
B. Kennedy, and A. Kuzmich, Nature (London) 438, 833 (2005).
[36] F. Vewinger, J. Appel, E. Figuera, and A. Lvovsky, Opt. Lett. 32,
2771 (2007).
[37] T. Peters, Y. H. Chen, J. S. Wang, Y. W. Lin, and I. A. Yu, Opt.
Lett. 35, 151 (2010).
[38] M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge
University Press, Cambridge, U.K., 1997).
[39] E. Merzbacher, Quantum Mechanics (John Wiley & Sons, 1998).
[40] Y. W. Lin, H. C. Chou, P. P. Dwivedi, Y.-C. Chen, and I. A. Yu,
Opt. Express 16, 3753 (2008).
[41] J. H. Wu, M. Artoni, and G. C. LaRocca, Phys. Rev. A 82, 013807
(2010).
[42] Y.-F. Chen, Y.-M. Kao, W.-H. Lin and I. A. Yu, Phys. Rev. A 74,
063801 (2006).
[43] R. Wei, B. Zhao, Y. Deng, S. Chen, Z.-B. Chen and J.-W. Pan,
Phys. Rev. A 81, 043403 (2010).
[44] John David Jackson, Classical Electrodynamics (Wiley; 3 edition,
1998).
[45] M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature 426, 638 (2003).
[46] S. E. Harris, Phys. Today 50, 36 (1997).
[47] F. E. Zimmer, A. Andre, M. D. Lukin, and M. Fleischhauer, Opt.
Commun. 264, 441 (2006).
[48] K. R. Hansen and K. Mlmer, Phys. Rev. A 75, 053802 (2007).
[49] K. R. Hansen and K. Mlmer, Phys. Rev. A 75, 065804 (2007).
[50] Y. Xue and B. S. Ham, Phys. Rev. A. 78, 053830 (2008).
[51] G. Nikoghosyan and M. Fleischhauer, Phys. Rev. A 80, 013818
(2009).
[52] S. A. Moissev and B. S. Ham, Phys. Rev. A 73, 33812 (2006).
[53] F. E. Zimmer, J. Otterbach, R. G. Unanyan, B. W. Shore, and M.
Fleischhauer, Phys. Rev. A 77, 063823 (2008).
[54] D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, Phys.
Rev. Lett. 93, 183601 (2004).
[55] M. Fleischhauer and M. D. Lukin, Phys. Rev. A 65, 22314 (2002).
[56] S. W. Su, Y. H. Chen, S. C. Gou, and I. A. Yu, J. Phys. B 44,
165504 (2011).
[57] S. W. Su, Y. H. Chen, S. C. Gou, T. L. Horng, and I. A. Yu, Phys.
Rev. A 83, 013827 (2011).
[58] S. N. Bose, Z. Phys. 26, 178 (1924).
[59] A. Einstein, Sitzungber, Kgl. Preuss. Akad. Wiss. (1924).
[60] M. H. Anderson, J. R. Ensher, M. R. Mattehews, C. E. Wieman,
and E. A. Cornell, Science 269, 198 (1995).
[61] K. B. Davis, M.-O, Mewes, M. R. Andrews, N. J. van Druten, D.
S. Durfee, D. M. Kurn, and W. Ketterle Phys. Rev. Lett. 75, 3969
(1995).
[62] K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard Phys.
Rev. Lett. 84, 806 (2000).
[63] I. Coddington, P. Engels, V. Schweikhard, and E. A. Cornell, Phys.
Rev. Lett. 91, 100402 (2003).
[64] S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock, A.
Sanpera, G. V. Shlyapnikov, and M. Lewenstein, Phys. Rev. Lett.
83, 5198 (1999).
[65] J. Stenger, S. Inouye, D. D. Stamper-Kurn, H.-J. Miesner, A. P.
Chikkatur, and W. Ketterle, Nature 396, 345 (1998).
[66] D.A.W. Hutcginson, E. Zaremba, and A. Grin, Phys. Rev. Lett.
78, 1842 (1997).
[67] B. Jackson and E. Zaremba, Phys. Rev. Lett. 88, 180402 (2000).
[68] W. H. Zurek, Nature 317, 505 (1983).
[69] T. W. B. Kibble, J. Phys. A 9, 1387 (1976).
[70] Davis M J, Ballagh R J and Burnett K, J. Phys. B:At. Mol. Opt.
Phys. 34, 4487 (2001).
[71] Gardiner C W, Anglin J R and Fudge T I A, J. Phys. B: At. Mol.
Opt. Phys. 35, 1555 (2002).
[72] Alice Sinatra, Carlos Lobo, and Yvan Castin, Phys. Rev. Lett. 87,
210404 (2001).
[73] D. M. Stamper-Kurn, M. R. Andrews, A. P. Chikkatur, S. Inouye,
H.-J. Miesner, J. Stenger, and W. Ketterle, Phys. Rev. Lett. 80,
2027 (1998).
[74] Masahito Ueda andMasato Koashi, Phys Rev. A 65, 063602 (2003).
[75] H. Schmaljohann, M. Erhard, J. Kronjager, M. Kottke, S. van Staa,
L. Cacciapuoti, J. J. Arlt, K. Bongs, and K. Sengstock, Phys. Rev.
Lett. 92, 040402 (2004).
[76] Hiroki Saito and Masahito Ueda, Phys. Rev. Lett. 72, 053628
(2005).
[77] Masashi Yasunaga and Makoto Tsubota, Phys. Rev. Lett. 101,
220401 (2008).
[78] Shoichi Hoshi and Hiroki Saito, Phys. Rev. A 81, 013627 (2010).
[79] U. Al Khawaja and H. T. C. Stoof, Phys. Rev. A 64, 043612 (2001).
[80] N. D. Mermin and Tin-Lun Ho, Phys. Rev. Lett. 36, 594 (1976).
[81] P. W. Anderson and G. Toulouse, Phys. Rev. Lett. 38, 508 (1977).
[82] T. Mizushima, N. Kobayashi, and K. Machida, Phys. Rev. A 70,
043613 (2004).
[83] T.-L. Horng, C.-H. Hsueh, S.-W. Su, Y.-M. Kao, and S.-C. Gou,
Phys. Rev. A 80, 023618 (2009).
[84] G. E. Volovik, The Universe in a Helium Droplet (Clarendon
Press, Oxford, 2003).
[85] D. A. Ivanov, Phys. Rev. Lett. 86, 268 (2001).
[86] U. K. RoBler al., Nature 442, 797 (2006).
[87] S. Muhlbauer et al., Science 323, 915 (2009).
[88] X. Z. Yu et al., Nature 465, 17 (2010).
[89] An-Chun Ji, W. M. Liu, Jun Liang Song, and Fei Zhou, Phys. Rev.
Lett. 101, 010402 (2008).
[90] T. P. Simula, Jukka A. M. Huhtamaki, Masahiro Takahashi,
Takeshi Mizushima, and Kazushige Machida, J. Phys. Soc. Jpn.
80, 013001 (2011).
[91] T.-L. Ho, Phys. Rev. Lett. 87, 060403 (2001).
[92] J. J. Sakurai, Modern Quantum Physics (Addison-Wesley Publishing
Company, Inc., U.S.A. 1994).
[93] Y.-J. Lin, K. Jimenez-Garcia and I. B. Spielman, Nature 471, 83
(2011).
[94] X.-J. Liu et al., Phys. Rev. Lett. 102, 046402 (2009).
[95] S. Bandyopadhyay, Phys. Rev. B 61, 13813 (2000).
[96] I. Zutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323
(2004).
[97] J. Sinova et al., Phys. Rev. Lett. 92, 126603 (2004).
[98] B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757
(2006).
[99] Y. Zhang et al., Nature Phys. 6, 584 (2010).
[100] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
[101] H. Hu et al., Phys. Rev. Lett. 108, 010402 (2012).
[102] C. Wang et al., Phys. Rev. Lett. 105, 160403 (2010).
[103] Z. F. Xu, R. Lu, and L. You, Phys. Rev. A 83, 053602 (2011).
[104] A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other
Topological Defects (Cambridge University Press, Cambridge, UK,
1994).
[105] T. Kawakami, T. Mizushima, and K. Machida, Phys. Rev. A 84,
011607(R) (2011).
[106] W. Yi and G.-C. Guo, Phys. Rev. A 84, 031608(R) (2011).
[107] L. Jiang et al., Phys. Rev. A 84, 063618 (2011).
[108] J. P. Vyasanakere and V. B. Shenoy, eprint arXiv:1108.4872v1.
[109] L. E. Sadler et al., Nature 443, 312 (2006).
[110] Chad N. Weiler et al., Nature 455, 948 (2008).
[111] C. Wang et al., Phys. Rev. Lett. 105, 160403 (2010).
[112] T. Mizushima, K. Marchida, and T. Kita, Phys. Rev. A 66, 053610
(2002).
[113] T. Kita, T. Mizushima, and K. Marchida, Phys. Rev. A 66,
061601(R) (2002).
[114] T. Mizushima, K. Marchida, and T. Kita, Phys. Rev. Lett. 89,
030401 (2002).
[115] G. E Brown and M. Rho, The Multifaced Skyrmion (World Scienti
c Singapore, 2010).
[116] Z. F. Xu, R. Lu, and L. You, Phys. Rev. A 83, 053602 (2011).
[117] T. Kibble, Physics Today 60, 47 (2007).
[118] R. Monaco, J. Mygind, and R. J. Rivers, Phys. Rev. Lett. 89,
080603 (2002).
[119] R. Monaco, J. Mygind, and R. J. Rivers, Phys. Rev. B 67, 104506
(2003).
[120] R. Monaco, M. Aaroe, J. Mygind, R. J. Rivers, and V. P.
Koshelets, Phys. Rev. B 74, 144513 (2006).
[121] R. Monaco, J. Mygind, M. Aaroe, R. J. Rivers, and V. P.
Koshelets, Phys. Rev. Lett. 96, 180604 (2006).
[122] W. H. Zurek, Phys. Rev. Lett. 102, 105702 (2009).
[123] A. del Campo, A. Retzker, and M. B. Plenio, New J. Phys. 13
083022 (2011).
[124] A. Das, J. Sabbatini and W. H. Zurek, Sci. Rep. 2, 352 (2012).
[125] B. Damski and W. H. Zurek, Phys. Rev. Lett. 104, 160404 (2010).
[126] J. Dziarmaga, J. Meisner, and W. J. Zurek, Phys. Rev. Lett. 101,
115701 (2008).
[127] J. Sabbatini, W. H. Zurek, and M. J. Davis, Phys. Rev. Lett. 107,
230402 (2011).
[128] D. Chen, M. White, C. Borries, and B. DeMarco, Phys. Rev. Lett.
106, 235304 (2011).
[129] M. E. Dodd, P. C. Hendry, N. S. Lawson, P. V. E. McClintock,
and C. D. H. Williams, Phys. Rev. Lett. 81, 3703 (1998).
[130] G. Karra and R. J. Rivers, Phys. Rev. Lett. 81, 3707 (1998); R.
J. Rivers, ibid. 84, 1248 (2000).
[131] L. M. A. Bettencourt, N. D. Antunes, and W. H. Zurek, Phys.
Rev. D. 62, 065005 (2000).
[132] P. Sikivie, Phys. Rev. Lett. 48, 1156 (1982).
[133] V. M. Kaurov and A. B. Kuklov, Phys. Rev. A 71, 011601(R)
(2005); ibid. 73, 013627 (2006).
[134] J. Brand, T. J. Haigh, and U. Zulicke, Phys. Rev. A 80, 011602(R)
(2009).
[135] A. Ramanathan, et. al., Phys. Rev. Lett. 106, 130401 (2011).
[136] T. Fernholz et. al., Phys. Rev. A 75, 063406 (2007).
[137] R. P. Anderson et. al., Phys. Rev. A 80, 023603 (2009).
[138] L. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Clarendon,
Oxford, 2003).
[139] M. I. Qadir, H. Susanto, P. C. Matthews, J. Phys. B 45, 035004
(2012).
[140] K. Henderson, C. Ryu, C. MacCormick and M. G. Boshier, New
J. Phys. 11, 043030 (2009).
[141] W. Zurek, Phys. Rep. 296, 177 (1996).
[142] D. J. Weir, R. Monaco, and R. J. Rivers, J. Low Temp. Phys.
DOI: 10.1007/s10909-012-0681-9 (2012); D. J. Weir, R. Monaco, V.
P. Koshelets, J. Mygind, and R. J. Rivers, e-print arXiv:1302:7296
(2013).
[143] G. Biroli, L. F. Cogliandolo, and A. Sicilia, Phys. Rev. E 81,
050101(R) (2010).
[144] M. Pospelov, S. Pustelny, M. P. Ledbetter, D. F. Jackson Kimball,
W. Gawlik, and D. Budker, Phys. Rev. Lett. 110, 021803 (2013).
[145] S. J. Rooney, P. B. Blakie, and A. S. Bradley, 86, 053634 (2012).