Quantum Control of Multi-Wave Mixing

Multi-wave mixing gives rise to new frequency components due to the interaction of light signals with a suitable nonlinear medium. In this book a systematic framework for the control of these processes is used to lead readers through a plethora of related effects and techniques.

Table of Contents:
Preface XI 1 Introduction 1 1.1 Suppression and Enhancement Conditions of the FWM Process 2 1.1.1 Dressed State Theory 2 1.1.2 Dark-State Theory in MWM Processes 4 1.1.3 Suppression and Enhancement Conditions 7 1.2 Fluorescence in MWM 10 1.3 MWM Process in Ring Optical Cavity 12 1.3.1 High-Order Cavity Mode Splitting with MWM Process 13 1.3.2 Squeezed Noise Power with MWM 14 1.3.3 Three-Mode Continuous-Variable Entanglement with MWM 16 1.4 Photonic Band Gap 17 1.4.1 Periodic Energy Level 18 1.4.2 Method of Transfer Matrix 19 1.4.3 Nonlinear Talbot Effect 20 1.4.4 Third- and Fifth-Order Nonlinearity 21 1.5 MWM with Rydberg Blockade 22 1.6 Summary 24 References 25 2 MWM Quantum Control via EIT 29 2.1 Interference of Three MWM via EIT 29 2.1.1 Experiment Setup 30 2.1.2 Basic Theory 31 2.1.3 Results and Discussions 33 2.1.4 Conclusion 39 2.2 Observation of EWM via EIT 40 2.2.1 Basic Theory 40 2.2.2 Experimental Results 41 2.2.3 Conclusion 46 2.3 Controlled MWM via Interacting Dark States 46 2.3.1 Basic Theory 47 2.3.2 Multi-Wave Mixing (MWM) 49 2.3.2.1 Four-Wave Mixing (FWM) 49 2.3.2.2 Four-Dressing SWM 53 2.3.2.3 Four-Dressing EWM 54 2.3.2.4 Four-Dressing EIT 55 2.3.3 Numerical Results and Discussion 55 2.3.3.1 Five-Dressing FWM 56 2.3.3.2 Four-Dressing SWM 62 2.3.3.3 Four-Dressing EWM 62 2.3.3.4 Absorption and Dispersion in the Four-Dressing EIT System 65 2.3.4 Discussion and Conclusion 67 2.4 Observation of Dressed Odd-Order MWM 68 2.4.1 Basic Theory and Experimental Scheme 68 2.4.2 Dressed Odd-Order MWM 70 2.4.3 Conclusion 87 References 87 3 Controllable Autler-Townes Splitting of MWM Process via Dark State 91 3.1 Measurement of ac-Stark Shift via FWM 91 3.1.1 Experiment and Basic Theory 92 3.1.2 Experiment and Result 95 3.1.3 Conclusion 96 3.2 Evidence of AT Splitting in FWM 97 3.2.1 Basic Theory 97 3.2.2 Experimental Results 99 3.3 Observation of AT Splitting in SWM 103 3.3.1 Theoretical Model and Experimental Scheme 103 3.3.2 Experiment and Result 106 3.3.3 Conclusion 110 References 110 4 Controllable Enhancement and Suppression of MWM Process via Dark State 113 4.1 Enhancing and Suppressing FWM in EIT Window 113 4.1.1 Theory and Experimental Results 114 4.1.2 Experiment and Result 115 4.1.3 Conclusion 119 4.2 Cascade Dressing Interaction of FWM Image 119 4.2.1 Theoretical Model and Experimental Scheme 120 4.2.2 Cascade Dressing Interaction 123 4.2.3 Conclusion 129 4.3 Multi-Dressing Interaction of FWM 130 4.3.1 Theoretical Model 131 4.3.2 Experimental Result 133 4.3.2.1 Single-Dressed DFWM 133 4.3.2.2 Doubly-Dressed DFWM 134 4.3.2.3 Triply-Dressed DFWM 139 4.3.2.4 Power Switching of Enhancement and Suppression 142 4.4 Enhancement and Suppression of Two Coexisting SWM Processes 144 4.4.1 Theoretical Model and Experimental Scheme 145 4.4.2 Experimental Results 147 4.4.3 Conclusion 153 References 154 5 Controllable Polarization of MWM Process via Dark State 157 5.1 Enhancement and Suppression of FWM via Polarized Light 157 5.1.1 Theoretical Model and Analysis 158 5.1.2 Experimental Results 160 5.1.3 Conclusion 164 5.2 Polarization-Controlled Spatial Splitting of FWM 165 5.2.1 Theoretical Model and Experimental Scheme 165 5.2.2 Spatial Splitting of FWM Beam 168 5.3 Coexisting Polarized FWM 172 5.3.1 Experiment Setup 172 5.3.2 Theoretical Model 173 5.3.3 Results and Discussions 178 5.4 Polarized Suppression and Enhancement of SWM 184 5.4.1 Theoretical Model and Experimental Scheme 184 5.4.2 Polarized Suppression and Enhancement 188 5.4.3 Conclusion 196 References 196 6 Exploring Nonclassical Properties of MWM Process 199 6.1 Opening Fluorescence and FWM via Dual EIT Windows 199 6.1.1 Theory and Experimental Scheme 200 6.1.2 Fluorescence and FWM via EIT Windows 202 6.2 Phase Control of Bright and Dark States in FWM and Fluorescence Channels 206 6.2.1 Theory and Experimental Scheme 206 6.2.2 Theory and Experimental Results 208 6.3 Observation of Angle Switching of Dressed FWM Image 211 6.3.1 Introduction 211 6.3.2 Theoretical Model and Experimental Scheme 212 6.3.3 Experimental Results and Theoretical Analyses 218 6.4 Three-Photon Correlation via Third-Order Nonlinear Optical Processes 227 6.4.1 Theory and Experimental Scheme 228 6.4.2 Theory and Experimental Results 229 6.4.3 Conclusion 232 6.5 Vacuum Rabi Splitting and Optical Bistability of MWM Signal Inside a Ring Cavity 232 6.5.1 Introduction 232 6.5.2 Basic Theory 233 6.5.3 VRS of Zero-Order Mode 235 6.5.3.1 Multi-Dressed VRS 235 6.5.3.2 Avoided Crossing Plots 237 6.5.3.3 Suppression and Enhancement of MWM 238 6.5.4 VRS of High-Order Modes 241 6.5.5 Steady-State Linear Gain and OPO Threshold 244 6.5.6 OB Behavior of MWM 246 6.5.6.1 OB of Zero-Order Mode 246 6.5.6.2 OB of High-Order Modes 248 6.5.7 Conclusion 251 References 251 7 Coherent Modulation of Photonic Band Gap in FWM Process 255 7.1 Spatial Interplay of Two FWM Images 255 7.1.1 Introduction 255 7.1.2 Theoretical Model and Experimental Scheme 256 7.1.3 The Interplay of Two FWM Beams 260 7.2 Optical Vortices Induced in Nonlinear Multi-Level Atomic Vapors 267 7.2.1 Introduction 267 7.2.2 Theoretical Model and Numerical Simulation 267 7.2.3 Conclusion 271 7.3 Multi-Component Spatial Vector Solitons of FWM 272 7.3.1 Basic Theory and Experimental Scheme 273 7.3.2 Experimental Observation of Multi-Component Solitons 277 7.3.3 Conclusion 285 7.4 Surface Solitons of FWM in EIL 285 7.4.1 Basic Theory and Experimental Scheme 286 7.4.2 Fluorescence and FWM via EIT Windows 289 7.4.3 Conclusion 294 7.5 Multi-Wave Mixing Talbot Effect 294 7.5.1 Introduction 294 7.5.2 Theoretical Model and Analysis 295 7.5.3 Suppression and Enhancement Conditions 297 7.5.4 Talbot Effect of MWM Signals 299 7.5.5 Conclusion 303 References 303 8 Optical Routing and Space Demultiplexer of MWM Process 311 8.1 Optical Switching and Routing 311 8.1.1 Introduction 311 8.1.2 Theoretical Model and Experimental Scheme 312 8.1.3 Optical Switching and Routing via Spatial Shift 314 8.2 All-Optical Routing and Space Demultiplexer 318 8.2.1 Theoretical Model and Experimental Scheme 318 8.2.2 Optical Switching and Routing 320 8.2.3 Conclusion 328 References 328 Index 331

About the Author :
Yangpeng Zhang Yangpeng Zhang received his PhD in Physics Electronics and Optical Electronics in 2000 and is now Tengfei Chair Professor at Xi'an Jiaotong University. He received numerous national science and technology young researchers awards for his theoretical studies on photonics, especially wave mixing. More than 100 papers in peer review journals and two books on all aspects of multi-wave mixing make him an ideal author for this topic. Feng Wen Feng Wen is currently PhD student at Xi'an Jiaotong University. Min Xiao Min Xiao is Distinguished Professor of Physics and holder of the 21st Century Chair in Nanotechnology at the University of Arkansas. He held positions in Shanxi University, China, and the Massachussetts Institute of Technology, received the NSF Young Investigator Award in 1994, and is a Fellow of the American Physical Society and the Optical Society of America. With more than 240 publications on related topics he is one of the experts in the field of multi-wave mixing.

Review :

“This text, supported by the two previous volumes published by the authors, will bring readers to the forefront of activity in this field.”  (Optics & Photonics News, 7 February 2014)