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1 Introduction 1

1.1 Nonlinear Susceptibility 1

1.2 Four-wave Mixing 5

1.3 Generalized Resonant MWM in Multi-level Atomic Systems 7

1.4 Enhanced Nonlinearity via Electromagnetically Induced Transparency 12

References 15

2 Femtosecond Polarization Beats 18

2.1 Effects of Field-correlation on Polarization Beats 18

2.1.1 PBFS in a Doppler-broadened System 23

2.1.2 Photon-echo 26

2.1.3 Experiment and Result 27

2.2 Correlation Effects of Chaotic and Phase-diffusion Fields 30

2.2.1 Photon-echo 38

2.2.2 Experiment and Result 41

2.3 Higher-order Correlations of Markovian Stochastic Fields on Polarization Beats 44

2.3.1 HOCPB in a Doppler-broadened System 50

2.3.2 Photon-echo 51

2.3.3 Experiment and Result 57

References 60

3 Attosecond Polarization Beats 63

3.1 Polarization Beats in Markovian Stochastic Fields 63

3.2 Perturbation Theory 66

3.3 Second-order Stochastic Correlation of SFPB 73

3.4 Fourth-order Stochastic Correlation of SFPB 88

3.5 Discussion and Conclusion 96

References 103

4 Heterodyne/Homodyne Detection of MWM 106

4.1 Modified Two-photon Absorption and Dispersion of Ultrafast Third-order Polarization Beats 106

4.1.1 Liouville Pathways 108

4.1.2 Color-locking Stochastic Correlations 113

4.1.3 Purely Homogeneously-broadened Medium 116

4.1.4 Extremely Doppler-broadened Limit 122

4.1.5 Discussion and Conclusion 130

4.2 Color-locking Phase Control of Fifth-order Nonljnear Response 131

4.3 Seventh-order Nonlinear Response 136

References 141

5 Raman- and Rayleigh-enhanced Polarization Beats 144

5.1 Raman-enhanced Polarization Beats 145

5.1.1 Chaotic Field 149

5.1.2 Raman Echo 154

5.1.3 Phase-diffusion Field 156

5.1.4 Gaussian-amplitude Field 159

5.1.5 Experiment and Result 166

5.2 Rayleigh-enhanced Attosecond Sum-frequency Polarization Beats 170

5.2.1 Stochastic Correlation Effects of RFWM 175

5.2.2 Homodyne Detection of Sum-frequency RASPB 188

5.2.3 Heterodyne Detection of the Sum-frequency RASPB 197

5.2.4 Discussion and Conclusion 202

References 205

6 Coexistence of MWM Processes via EIT Windows 207

6.1 Opening FWM and SWM Channels 207

6.2 Enhancement of SWM by Atomic Coherence 216

6.3 Observation of Interference between FWM and SWM 223

6.4 Controlling FWM and SWM Processes 227

References 233

7 Interactions of MWM Processes 235

7.1 Competition between Two FWM Channels 235

7.2 Efficient Energy Transfer between FWM and SWM Processes 242

7.3 Spatial and Temporal Interferences between Coexisting FWM and SWM Signals 251

References 258

8 Multi-dressed MWM Processes 261

8.1 Matched Ultraslow Pulse Propagations in Highly-Efficient FWM 261

8.1.1 Time-dependent,Adiabatic Treatment for Matched Probe and NDFWM Signal Pulses 267

8.1.2 Steady-state Analysis 273

8.1.3 Discussion and Outlook 281

8.2 Generalized Dressed and Doubly-dressed MWM Processes 283

8.2.1 Generalized Dressed-(2n-2)WM and Doubly-dressed-(2n-4)WM Processes 284

8.2.2 Interplays Among Coexisting FWM,SWM,and EWM Processes 287

8.3 Interacting MWM Processes in a Five-level System with Doubly-dressing Fields 292

8.3.1 Three Doubly-Dressing Schemes 294

8.3.2 Aulter-Townes Splitting,Suppression,and Enhancement 299

8.3.3 Competition between Two Coexisting Dressed MWM 307

8.3.4 Conclusion and Outlook 313

References 315

Index 317