電磁誘發透明與多分量玻色愛因斯坦凝聚體在非零溫動力學的理論研究

Theoretical studies on the dynamics of electromagnetically induced transparency and multi-component Bose-Einstein condensates at non-zero temperatures

蘇士煒(Shih-Wei Su)

指導教授 ： 郭西川 ； 余怡德

國立清華大學/理學院/物理學系/博士(2013年)

https://doi.org/10.6843/NTHU.2013.00207

摘要

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。

關鍵字

電磁誘發透明 ； 玻色愛因斯坦凝聚體

並列摘要

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.

參考文獻

Phys. Rev. Lett. 83, 1767 (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).