雙里德堡 EIT 系統和 Exciton-Polariton 玻色-愛因斯坦凝聚體中交叉相位調製的理論研究

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研究生：	蘇希爾 Adhikari, Sushil
論文名稱：	雙里德堡 EIT 系統和 Exciton-Polariton 玻色-愛因斯坦凝聚體中交叉相位調製的理論研究 Theoretical Studies on Cross-Phase Modulation in Double Rydberg EIT Systems and the Exciton-Polariton BEC
指導教授：	余怡德 Yu, Ite A.
口試委員:	童世光 Tung, Shih-Kuang 廖文德 Liao, Wen-Te
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2023
畢業學年度：	111
語文別：	英文
論文頁數：	109
中文關鍵詞：	雙里德伯格 EIT
外文關鍵詞：	Double Rydberg EIT, Electromagentically Induced Transparency, Cross phase Modulation, Polariton BEC
相關次數：	點閱：3 下載：0
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篇文主要在量子光和凝聚物理域行了理研究，注Rydberg磁感透明度（EIT）系中的交叉相位制（XPM）和激子极化子的玻色-因斯坦凝聚（BEC）。
文的第一部分首先介了EIT和偶极-偶极相互作用（DDI）。文章了三Λ-EIT系，包括其性以及在慢光和光存中的用。然后解了Rydberg EIT系中DDI象。接，提出了具有DDI的Rydberg方案的理公式。了研究在各种件和型下信的和相位移，行了值模。通定优越性因（FOM）相位移和衰的比率，比了并优化了信的XPM。果示，如信中的光子失（∆c2）、耦合度和配置等因素在影信的XPM上起的作用。
文的第二部分了激子-极化子BEC的理方面。述了BEC的基本原，特性，以及在冷原子蒸气中BEC的技。然后全面回了激子-极化子BEC，包括于激子、极化子及其系形成的信息。探索了3D盒和3D振下BEC的件。已推出BEC中度与能量空之的一般系，以及在不同捕下的凝聚界密度。同也研究了在2D系（例如激子-极化子）中BEC凝聚的件，并且研究果支持了回文中的果。

This thesis presents two theoretical investigations in quantum optics and condensed matter physics, focusing on cross-phase modulation (XPM) in a double Rydberg electromagnetically induced transparency (EIT) system and Bose-Einstein condensation (BEC) of exciton polaritons.

The first part of the thesis provides an introduction to EIT and dipole-dipole interaction (DDI). The three-level Λ-EIT system is discussed, including its properties and application in slow light and light storage. The phenomenon of DDI in the Rydberg EIT system is also explained. The theoretical formulation of a double Rydberg scheme with DDI is then presented. Numerical simulations are conducted to study the transmission and phase shift of the signal field under various conditions and pulse types. A figure of merit (FOM), defined
as the ratio of phase shift to attenuation, is used to compare parameters and optimize signal XPM. The results show that factors such as one-photon detuning in the signal (Δc2), coupling strengths, and pulse configuration play crucial roles in influencing the XPM of the signal field.

The second part of the thesis discusses the theoretical aspects of exciton-polariton BEC. The basic principles of BEC, its characteristics, and the techniques for achieving BEC in cold atom vapor are outlined. A comprehensive review of exciton-polariton BEC is then presented, including details on excitons, polaritons, and their system formation. The conditions for BEC in case of 3D box potential and a 3D harmonic potential, are explored. A general relationship
between temperature and energy space in BEC, and the critical density for condensation at different trapping potentials has been derived. The conditions for realizing a BEC-like condensation in a 2D system such as exciton-polaritons are also studied, and the findings
supports the results from reviewed literature.

Contents
Acknowledgements (Chinese) I
Abstract (Chinese) II
Acknowledgements III
Abstract IV
Contents V
I Theoretical Study on Cross-Phase Modulation in Double
Rydberg EIT System 1
Introduction 2
1 Background of Study . . . . . . . . . . . . . . . . . . . . . 2
2 Motivation and Scope . . . . . . . . . . . . . . . . . . . . . 4
EIT system and Dipole interaction ...............................5
1 Theory of Three-level Λ-EIT system . . . . . . . . . . . . .  5
1.1 Optical Bloch equation . . . . . . . . . . . . . . . . . . .  6
1.2 Relating microscopic and macroscopic properties . . . . . . . . . . . . . 10
1.3 Transmission and Dispersion profile of EIT . . . . . . . . . . . . . . . . 11
1.4 Slow light and light storage . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Slow and retrieved light of Gaussian-pulse probe in single Λ system . . 16
2 Dipole-Dipole interaction in Rydberg EIT . . . . . . . . . . . . . . . . . . . . 17
2.1 Properties of Rydberg atom . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Theory of 3 level Rydberg EIT . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Mean field theory of 3 level Rydberg EIT with DDI . . . . . . . . . . . 21
2.4 Figure of Merit(FOM) for Phase Modulation . . . . . . . . . . . . . . . 27
3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Double Rydberg Scheme with DDI 30
1 Optical Bloch Equation for Double Rydberg Scheme . . . . . . . . . . . . . . . 30
2 OBE with perturbative limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 Analytical solution for perturbed OBE’s and MSE’s . . . . . . . . . . . . . . . 37
4 Optimization condition for phase and FOM . . . . . . . . . . . . . . . . . . . 37
5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Numerical Simulation-Parameter Estimation 39
1 CW steady state probe and signal field . . . . . . . . . . . . . . . . . . . . . . 39
2 Gaussian signal pulse and CW steady state probe . . . . . . . . . . . . . . . . 51
2.1 Role Gaussian pulse width in phase and FOM . . . . . . . . . . . . . . 53
2.2 Reduced transmission and pulse delay DDI . . . . . . . . . . . . . . . 55
3 Gaussian probe and Gaussian signal pulse . . . . . . . . . . . . . . . . . . . . 57
3.1 Attenuation and phase with Δc2 . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Optimization of Ωc2 for reduced width 30(1/Γ) . . . . . . . . . . . . . 59
3.3 Optimization for same input pulse energy but varied width and amplitude 60
4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Conclusion

II Theoretical Study on the Exciton-Polariton BEC 66
Introduction 67
1 Bose-Einstein Condensation (BEC) . . . . . . . . . . . . . . . . . . . . . . . . 67
1.1 Basic Concepts of BEC . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
1.2 Characteristics of BEC . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2 Realization of BEC in Cold Atom Vapor . . . . . . . . . . . . . . . . . . . . . 69
3 Review on Excition polariton . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.1 Excitons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.2 Polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.3 Exciton-Polariton System: Formation and Bosonic Nature . . . . . . . 73
4 Motivation and Scope of the Study . . . . . . . . . . . . . . . . . . . . . . . . 73
BEC condition for different potential 75
1 Ideal Bose gas (3D box potential) . . . . . . . . . . . . . . . . . . . . . . . . . 75
1.1 Expression for Critical Density . . . . . . . . . . . . . . . . . . . . . . 77
2 Three-dimensional Harmonic Potential . . . . . . . . . . . . . . . . . . . . . . 78
2.1 Temperature and Energy Spacing Relation in the Context of BEC . . . 79
2.2 Relation of Fugacity and Occupancy with temperature . . . . . . . . . 80
2.3 Effective Volume and Critical density for Harmonic trap . . . . . . . . 85
3 BEC in 2D and the Role of Potential Traps . . . . . . . . . . . . . . . . . . . 86
3.1 BEC in 2D System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.2 BEC in 2D System with a Harmonic Trap . . . . . . . . . . . . . . . . 87
4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Conclusion 90
Bibliography 92
Appendix A 95
Appendix B 100
B BEC of exciton polaritons, J. Kasprzak et al. . . . . . . . . . . . . . . . . . . . 100
B.1 Exciton and Cavity photon Interactions . . . . . . . . . . . . . . . . . . 101
B.2 Exciton Polaritons Condensation in 2D . . . . . . . . . . . . . . . . . . 103
B.3 Need of Local minima due to disorder in wells . . . . . . . . . . . . . . 104
B.4 Power Driven Phase Transition and BEC Indication . . . . . . . . . . . 105
B.5 Test for Condensate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

                                

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