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

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

1. Introduction

The Characteristics and applications of EIT medium  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 EIT: electromagnetically induced transparency

 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] Energy level  If add another stronger control field that effect the quantum interference between two paths, inhibiting the absorption of probe field by medium. [Kocharovskaya ， Harris] What is EIT ？ Why do the EIT being important ？  1. Introduction 1.2 EIT EIT  Changing the dispersion relationship, the absorption and group velocity  Enhanced the Kerr nonlinearity

2 ． General theory of the interaction between light and atom

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

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

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

2.General theory  AVE and Maxwell equations

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

2.3.2 EIT 2.General theory Parameters ：

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

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

Transient optical property of four-level atom  Model

Transient optical property of four-level atom  Nonlinear susceptibility

4. Two-component optical solitons in four-level Ladder system  Hui-jun Li and Guoxiang Huang, Two-Component Spatial Optical Solitons in a Four-State Ladder System via Electromagnetically Induced Transparency, Physics Letters A 22, 4127 (2008).

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

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

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

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

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

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

5. Highly efficiency four-wave mixing （ FWM ） in a coherent six-level system  Hui-jun Li and Guoxiang Huang, Highly Efficient Four-Wave Mixing in a Coherent Six- Level System in Ultraslow Propagation Regime, Physical Review A 76, (2007).

Highly efficiency FWM  Model

Highly efficiency FWM  Dispersion relationship  Parameters:

The conversion efficiency of FWM Highly efficiency FWM

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

Comparison (2)

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

Comparison the analytic result with numerical simulation result Highly efficiency FWM

 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 conclusion

The finished papers during doctoral studying  1. Hui-jun Li and Guoxiang Huang, Highly Efficient Four-Wave Mixing in a Coherent Six- Level System in Ultraslow Propagation Regime, Physical Review A 76, (2007).  2. Hui-jun Li, Chao Hang, and Guoxiang Huang, Transient optical properties of coherent four- level atoms without undepleted ground-state approximation, Physics Letters A 368, 336 (2007).  3. Hui-jun Li and Guoxiang Huang, Two-Component Spatial Optical Solitons in a Four-State Ladder System via Electromagnetically 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-Assisted Superluminal Optical Solitons in Three-Level Systems, submitted to Physical Review A,  5. Guoxiang Huang, Hui-jun Li, and L. Deng, Dynamics of Ultraslow Optical Solitons in a Cold Four-State Double Lambda System via Electromagnetically Induced Transparency, submitted to Physical Review A,  6. Hui-jun Li and Guoxiang Huang, Modulational Instability and the Generation of Ultraslow Optical Solitons in Coherent Atomic Systems, in preparation.

Thank you ！