Title ： Investigation on Nonlinear Optical Effects of Weak Light in Coherent Atomic Media

1. Title：Investigation on Nonlinear Optical Effects of Weak Light in Coherent Atomic Media Author：Hui-jun Li Supervisor: Prof Guoxiang Huang Subject: Theoretical Physics Field of Study: Nonlinear Physics and Nonlinear Optics

2. Outline • 1. Introduction • 2. General theory of light field propagation in cold atom gas medium • 3. Transient Optical Properties of Coherent Four-Level Atoms • 4. Two-component spatial optical solitons in a four-state ladder system • 5. Highly efficient four-wave mixing in a coherent six-level system • 6. Conclusion

3. 1. Introduction

4. The Characteristics and applications of EIT medium EIT: electromagnetically induced transparency • Controlled the absorpsion of probe field by atomic medium →Switching of all light S. E. Harris Y. F. Zhu • Changed the group velocity of probe field →Stored light pulsed M. Fleischhauer & M. D. Lukin L. V. Hau →Compression of light pulse D. F. Phillips • Enhanced the Kerr nonlinearity of medium →Highly efficiency multi-wave mixing Harris & Lukin, L.Deng, Y. Wu →Optical solitons Wu & Deng, G. X. Huang →The quantum phase gate and quantum computer Ottaviani Petrosyan • Others applications： →Controllable gap solitons Lukin →Precision optical clock J. Ye →Cold molecular condensates H. Pu & W. P. Zhang →Transient and optical chaos M. Xiao

5. 1. Introduction 1.2 EIT What is EIT？ Energy level • When a weak and width probed pulse is injected into two-level atomic medium, the light field will be absorbed by the atomic system, that is, the medium is not transparency. • Self induced transparency: when a stronger and shorter pulse injecting into two-level medium. the field can be passed without any absorption. [MacCall & Hahn, 1967] EIT If add another stronger control field that effect the quantum interference between two paths, inhibiting the absorption of probe field by medium. [Kocharovskaya，Harris] Why do the EIT being important？ Changing the dispersion relationship, the absorption and group velocity Enhanced the Kerr nonlinearity

6. 2．General theory of the interaction between light and atom

7. 2.General theory Electric field There are three internal-states (j=1,2,3) They are complete and orthogonal base vector. Hamiltonian of system： State function Polarization strength

8. 2.General theory Phase match condition and rotating wave approximation, and defined the half-Rabi frequency They are the amplitude variable equations (AVE).

9. 2.Genral theory Field satisfies Maxwell equation Considering the field form and polarization， here, we adopt the slowly-variable envelope approximation，

10. 2.General theory AVE and Maxwell equations

11. 2.General theory 2.3.2 EIT Model Considering the atoms populate in the ground state， field p is weaker，and c field is stronger, we neglect the ground state depletion, we can get the Making Fourier transformation dispersion relationship

12. 2.General theory 2.3.2 EIT Parameters：

13. 2. General theory 2.3.3 the linear propagation of probe field Making Taylor expansion of K(w) around w=0, If initial probed field

14. 3. Transient optical property of four-level atom Hui-jun Li,Chao Hang, and Guoxiang Huang, Transientoptical properties of coherent four- level atoms without undepletedground-state approximation, Physics Letters A 368, 336(2007).

15. Transient optical property of four-level atom Model

16. Transient optical property of four-level atom Nonlinear susceptibility

17. 4. Two-component optical solitons in four-level Ladder system Hui-jun Li and Guoxiang Huang, Two-Component SpatialOptical Solitons in a Four-StateLadder System viaElectromagnetically Induced Transparency,Physics Letters A 22, 4127(2008).

18. Two-component optical solitons in four-level Ladder system Model Stable state： Asymptotic expansion：

19. two-component optical solitons in four-level Ladder system In first order, we can get To third order, combining every order results, we can get coupled Ginzberg-Landau equation

20. two-component optical solitons in four-level Ladder system Spatial optical solitons Single-component solitons If we can find the bright soliton

21. two-component optical solitons in four-level Ladder system The evolution of spatial solitons with the increase distance Parameters：

22. two-component optical solitons in four-level Ladder system Two-component solitons we can get four-kinds of soliton pair solutions If Bright-bright solitons： are arbitrary constant.

23. two-component optical solitons in four-level Ladder system Evolution of two-component spatial soliton with the distance z Parameters：

24. 5. Highly efficiency four-wave mixing（FWM）in a coherent six-level system Hui-jun Li and Guoxiang Huang, Highly Efficient Four-WaveMixing in a Coherent Six- Level System in UltraslowPropagationRegime, Physical Review A76, 043809(2007).

25. Highly efficiency FWM Model

26. Highly efficiency FWM Dispersion relationship Parameters:

27. Highly efficiency FWM The conversion efficiency of FWM

28. Highly efficiency FWM Comparison of the FWM efficiency in different system (1)

29. Highly efficiency FWM Comparison (2)

30. Highly efficiency FWM Generating process of the FWM field and the energy exchange between fields

31. Highly efficiency FWM Comparison the analytic result with numerical simulation result

32. conclusion • Transient Optical Properties of Coherent Four-Level Atoms • Two-component spatial optical solitons in a four-state system • Highly efficient four-wave mixing in a coherent six-level system

33. The finished papers during doctoral studying 1. Hui-jun Li and Guoxiang Huang, Highly Efficient Four-WaveMixing in a Coherent Six- Level System in UltraslowPropagationRegime, Physical Review A76, 043809(2007). 2. Hui-jun Li,Chao Hang, and Guoxiang Huang, Transientoptical properties of coherent four- level atoms without undepletedground-state approximation, Physics Letters A 368, 336(2007). 3. Hui-jun Li and Guoxiang Huang, Two-Component SpatialOptical Solitons in a Four-State Ladder System viaElectromagnetically Induced Transparency,Physics Letters A 22, 4127(2008). 4. Hui-jun Li,Chao Hang, L. Deng, and Guoxiang Huang, High-Order Nonlinear Schrodinger Equation and Gain-AssistedSuperluminal Optical Solitons in Three-Level Systems, submittedto Physical Review A,2008. 5. Guoxiang Huang,Hui-jun Li, and L. Deng, Dynamics ofUltraslow Optical Solitons in a Cold Four-State Double LambdaSystem via Electromagnetically Induced Transparency, submittedto Physical Review A, 2008. 6. Hui-jun Li and Guoxiang Huang, Modulational Instabilityand the Generation of Ultraslow Optical Solitons in CoherentAtomic Systems, in preparation.

34. Thank you！