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
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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
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1. Introduction
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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
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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
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2 General theory of the interaction between light and atom
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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
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2.General theory Phase match condition approximation, and
defined the half-Rabi frequency and rotating wave They are the
amplitude variable equations (AVE).
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2.Genral theory Field satisfies Maxwell equation Considering
the field form and polarization here, we adopt the slowly-variable
envelope approximation
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2.General theory AVE and Maxwell equations
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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
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2.3.2 EIT 2.General theory Parameters
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2.3.3 the linear propagation of probe field 2. General theory
Making Taylor expansion of K( ) around =0, If initial probed
field
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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).
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Transient optical property of four-level atom Model
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Transient optical property of four-level atom Nonlinear
susceptibility
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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).
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Two-component optical solitons in four-level Ladder system
Model Stable state Asymptotic expansion
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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
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Spatial optical solitons Single-component solitons If we can
find the bright soliton two-component optical solitons in
four-level Ladder system
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The evolution of spatial solitons with the increase distance
Parameters two-component optical solitons in four-level Ladder
system
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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
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Evolution of two-component spatial soliton with the distance z
Parameters two-component optical solitons in four-level Ladder
system
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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, 043809 (2007).
The conversion efficiency of FWM Highly efficiency FWM
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Comparison of the FWM efficiency in different system (1) Highly
efficiency FWM
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Comparison (2)
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Generating process of the FWM field and the energy exchange
between fields Highly efficiency FWM
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Comparison the analytic result with numerical simulation result
Highly efficiency FWM
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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
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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, 043809 (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, 2008. 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, 2008. 6. Hui-jun Li and Guoxiang
Huang, Modulational Instability and the Generation of Ultraslow
Optical Solitons in Coherent Atomic Systems, in preparation.
