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1 Classical Electromagnetic Fields 1

1.1 Maxwell's Equations in a Vacuum 2

1.2 Maxwell's Equations in a Medium 4

1.3 Linear Dipole Oscillator 10

1.4 Coherence 17

1.5 Free-Electron Lasers 22

Problems 32

2 Classical Nonlinear Optics 35

2.1 Nonlinear Dipole Oscillator 35

2.2 Coupled-Mode Equations 38

2.3 Cubic Nonlinearity 40

2.4 Four-Wave Mixing with Degenerate Pump Frequencies 43

2.5 Nonlinear Susceptibilities 48

Problems 50

3 Quantum Mechanical Background 51

3.1 Review of Quantum Mechanics 52

3.2 Time-Dependent Perturbation Theory 64

3.3 Atom-Field Interaction for Two-Level Atoms 71

3.4 Simple Harmonic Oscillator 82

Problems 86

4 Mixtures and the Density Operator 93

4.1 Level Damping 94

4.2 The Density Matrix 98

4.3 Vector Model of Density Matrix 106

Problems 112

5 CW Field Interactions 117

5.1 Polarization of Two-Level Medium 117

5.2 Inhomogeneously Broadened Media 124

5.3 Counterpropagating Wave Interactions 129

5.4 Two-Photon Two-Level Model 133

5.5 Polarization of Semiconductor Gain Media 139

Problems 146

6 Mechanical Effects of Light 151

6.1 Atom-Field Interaction 152

6.2 Doppler Cooling 157

6.3 The Near-Resonant Kapitza-Dirac Effect 158

6.4 Atom Interferometry 166

Problems 169

7 Introduction to Laser Theory 171

7.1 The Laser Self-Consistency Equations 172

7.2 Steady-State Amplitude and Frequency 175

7.3 Standing-Wave,Doppler-Broadened Lasers 181

7.4 Two-Mode Operation and the Ring Laser 187

7.5 Mode Locking 191

7.6 Single-Mode Semiconductor Laser Theory 194

7.7 Transverse Variations and Gaussian Beams 198

Problems 203

8 Optical Bistability 209

8.1 Simple Theory of Dispersive Optical Bistability 210

8.2 Absorptive Optical Bistability 215

8.3 Ikeda Instability 217

Problems 220

9 Saturation Spectroscopy 223

9.1 Probe Wave Absorption Coefficient 224

9.2 Coherent Dips and the Dynamic Stark Effect 230

9.3 Inhomogeneously Broadened Media 238

9.4 Three-Level Saturation Spectroscopy 241

9.5 Dark States and Electromagnetically Induced Transparency 244

Problems 247

10 Three and Four Wave Mixing 249

10.1 Phase Conjugation in Two-Level Media 250

10.2 Two-Level Coupled Mode Coefficients 253

10.3 Modulation Spectroscopy 255

10.4 Nondegenerate Phase Conjugation by Four-Wave Mixing 259

Problems 260

11 Time-Varying Phenomena in Cavities 263

11.1 Relaxation Oscillations in Lasers 264

11.2 Stability of Single-Mode Laser Operation 267

11.3 Multimode Mode Locking 271

11.4 Single-Mode Laser and the Lorenz Model 274

Problems 276

12 Coherent Transients 281

12.1 Optical Nutation 282

12.2 Free Induction Decay 284

12.3 Photon Echo 285

12.4 Ramsey Fringes 288

12.5 Pulse Propagation and Area Theorem 289

12.6 Self-Induced Transparency 293

12.7 Slow Light 295

Problems 296

13 Field Quantization 299

13.1 Single-Mode Field Quantization 299

13.2 Multimode Field Quantization 302

13.3 Single-Mode Field in Thermal Equilibrium 304

13.4 Coherent States 307

13.5 Coherence of Quantum Fields 311

13.6 Quasi-Probability Distributions 314

13.7 Schr？dinger Field Quantization 318

13.8 The Gross-Pitaevskii Equation 322

Problems 324

14 Interaction Between Atoms and Quantized Fields 327

14.1 Dressed States 328

14.2 Jaynes-Cummings Model 333

14.3 Spontaneous Emission in Free Space 338

14.4 Quantum Beats 344

Problems 348

15 System-Reservoir Interactions 351

15.1 Master Equation 353

15.2 Fokker-Planck Equation 362

15.3 Langevin Equations 364

15.4 Monte-Carlo Wave Functions 369

15.5 Quantum Regression Theorem and Noise Spectra 374

Problems 379

16 Resonance Fluorescence 383

16.1 Phenomenology 384

16.2 Langevin Equations of Motion 387

16.3 Scattered Intensity and Spectrum 390

16.4 Connection with Probe Absorption 396

16.5 Photon Antibunching 400

16.6 Off-Resonant Excitation 403

Problems 405

17 Squeezed States of Light 409

17.1 Squeezing the Coherent State 410

17.2 Two-Sidemode Master Equation 414

17.3 Two-Mode Squeezing 417

17.4 Squeezed Vacuum 421

Problems 425

18 Cavity Quantum Electrodynamics 427

18.1 Generalized Master Equation for the Atom-Cavity System 428

18.2 Weak Coupling Regime 430

18.3 Strong Coupling Regime 432

18.4 Velocity-Dependent Spontaneous Emission 435

18.5 Input-Output Formalism 440

Problems 443

19 Quantum Theory of a Laser 445

19.1 The Micromaser 447

19.2 Single Mode Laser Master Equation 454

19.3 Laser Photon Statistics and Linewidth 460

19.4 Quantized Sidemode Buildup 468

Problems 470

20 Entanglement,Bell Inequalities and Quantum Information 473

20.1 Einstein-Podolsky-Rosen Paradox and Bell Inequalities 473

20.2 Bipartite Entanglement 477

20.3 The Quantum Beam Splitter 480

20.4 Quantum Teleportation 483

20.5 Quantum Cryptography 484

20.6 Toward Quantum Computing 486

Problems 488

References 489

Index 499