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劍橋2011Manipulating.Quantum.Structures.Using.Laser.Pulses
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Preface page xi Acknowledgments xiii 1 Introduction 1 1.1 Objective 1 1.2 Background 1 1.3 Measurables, observables, and parameters 2 1.4 Notation and nomenclature 5 1.5 Limitations of the theory 7 1.6 Basic references 8 2 Atoms as structured particles 9 2.1 Spectroscopy 10 2.2 Quantum states 13 2.3 Probabilities 15 3 Radiation 19 3.1 Thermal radiation; quanta 19 3.2 Cavities 20 3.3 Incoherent radiation 21 3.4 Laser radiation 22 3.5 Laser fields 23 3.6 Field vectors 31 3.7 Laser beams 40 3.8 Photons 41 3.9 Field restrictions 43 4 The laser–atom interaction 44 4.1 Individual atoms 44 4.2 Detecting excitation 50 v vi Contents 4.3 The interaction energy; multipole moments 52 4.4 Moving atoms 54 5 Picturing quantum structure and changes 57 5.1 Free electrons: Ponderomotive energy 57 5.2 Picturing bound electrons 58 5.3 The Lorentz force 61 5.4 The wavefunction; orbitals 62 5.5 The statevector; Hilbert spaces 66 5.6 Two-state Hilbert spaces 69 5.7 Time-dependent statevectors 73 5.8 Picturing quantum transitions 76 6 Incoherence: Rate equations 78 6.1 Thermalized atoms; the Boltzmann equation 78 6.2 The radiative rate equations 79 6.3 The Einstein rates 79 6.4 The two-state rate equations 81 6.5 Solutions to the rate equations 81 6.6 Comments 83 7 Coherence: The Schrödinger equation 85 7.1 Essential states; effective Hamiltonians 87 7.2 The coupled differential equations 88 7.3 Classes of interaction 93 7.4 Classes of solutions 93 7.5 The time-evolution matrix; transition probabilities 95 8 Two-state coherent excitation 97 8.1 The basic equations 97 8.2 Abrupt start 104 8.3 The rotating-wave approximation (RWA) 108 8.4 Adiabatic time evolution 118 8.5 Comparison of excitation methods 135 9 Weak pulse: Perturbation theory 137 9.1 Weak resonant excitation 138 9.2 Pulse aftermath and frequency content 138 9.3 Example: Excitation despite missing frequencies 139 9.4 The Dirac (interaction) picture 141 9.5 Weak broadband radiation; transition rates 142 9.6 Fermi’s famous Golden Rule 144 10 The vector model 146 10.1 The Feynman–Vernon–Hellwarth equations 146 10.2 Coherence loss; relaxation 150 Contents vii 11 Sequential pulses 159 11.1 Contiguous pulses 159 11.2 Pulse trains 160 11.3 Examples 162 11.4 Pulse pairs 163 11.5 Vector picture of pulse pairs 165 11.6 Creating dressed states 167 11.7 Zero-area pulses 168 12 Degeneracy 171 12.1 Zeeman sublevels 171 12.2 Radiation polarization and selection rules 172 12.3 The RWA with degeneracy 177 12.4 Optical pumping 179 12.5 General angular momentum 181 13 Three states 186 13.1 Three-state linkages 186 13.2 The three-state RWA 188 13.3 Resonant chains 197 13.4 Detuning 201 13.5 Unequal Rabi frequencies 211 13.6 Laser-induced continuum structure (LICS) 218 14 Raman processes 222 14.1 The Raman Hamiltonian 222 14.2 Population transfer 223 14.3 Explaining STIRAP 230 14.4 Demonstrating STIRAP 235 14.5 Optimizing STIRAP pulses 237 14.6 Two-state versions of STIRAP 239 14.7 Extending STIRAP 243 15 Multilevel excitation 253 15.1 Multiphoton and multiple-photon ionization 253 15.2 Coherent excitation of N-state systems 255 15.3 Chains 259 15.4 Branches 277 15.5 Loops 287 15.6 Multilevel adiabatic time evolution 292 16 Averages and the statistical matrix (density matrix) 299 16.1 Ensembles and expectation values 299 16.2 Statistical averages 300 16.3 Environmental averages 302 viii Contents 16.4 Expectation values 304 16.5 Uncertainty relations 307 16.6 The density matrix 308 16.7 Density matrix equation of motion 313 16.8 Incorporating incoherent processes 317 16.9 Rotating coordinates 321 16.10 Multilevel generalizations 324 17 Systems with parts 331 17.1 Separability and factorization 331 17.2 Center of mass motion 333 17.3 Two parts 338 17.4 Correlation and entanglement 343 18 Preparing superpositions 347 18.1 Superposition construction 347 18.2 Nondegenerate states 348 18.3 Degenerate discrete states 350 18.4 Transferring superpositions 351 18.5 State manipulations using Householder reflections 352 19 Measuring superpositions 357 19.1 General remarks 357 19.2 Spin matrices and quantum tomography 359 19.3 Two-state superpositions 362 19.4 Analyzing multistate superpositions 364 19.5 Analyzing three-state superpositions 366 19.6 Alternative procedures 368 20 Overall phase; interferometry and cyclic dynamics 370 20.1 Hilbert-space rays 371 20.2 Parallel transport 372 20.3 Phase definition 373 20.4 Michelson interferometry 374 20.5 Alternative interferometry 377 20.6 Ramsey interferometry 378 20.7 Cyclic systems 379 21 Atoms affecting fields 387 21.1 Induced dipole moments; propagation 387 21.2 Single field, N= 2 389 21.3 Multiple fields 402 21.4 Two or three fields, N = 3 403 Contents ix 21.5 Four fields, N = 4; four-wave mixing 410 21.6 Steady state; susceptibility 413 22 Atoms in cavities 419 22.1 The cavity 420 22.2 Two-state atoms in a cavity 423 22.3 Three-state atoms in a cavity 429 23 Control and optimization 435 23.1 Control theory 435 23.2 Quantum control 436 23.3 Optimization 439 Appendix A Angular momentum 442 A.1 Angular momentum states 442 A.2 Angular momentum coupling 451 A.3 Hyperfine linkages 456 Appendix B The multipole interaction 459 B.1 The bound-particle interaction 459 B.2 The multipole moments 462 B.3 Examples 464 B.4 Induced moments 464 B.5 Irreducible tensor form 465 B.6 Rabi frequencies 465 B.7 Angular momentum selection rules 466 Appendix C Classical radiation 468 C.1 The Lorentz force; Maxwell’s equations 468 C.2 Wave equations 470 C.3 Frequency components 476 C.4 The influence of matter 480 C.5 Pulse-mode expansions 482 Appendix D Quantized radiation 487 D.1 Field quantization 488 D.2 Mode fields 496 D.3 Photon states 505 D.4 The free-field radiation Hamiltonian 507 D.5 Interpretation of photons 509 Appendix E Adiabatic states 513 E.1 Terminology 513 E.2 Adiabatic evolution 515 E.3 The Dykhne–Davis–Pechukas (DDP) formula 519 x Contents Appendix F Dark states; the Morris–Shore transformation 522 F.1 The Morris–Shore transformation 522 F.2 Bright and dark states 524 F.3 Fan linkages 526 F.4 Chain linkages 526 F.5 Generalizations 527 Appendix G Near-periodic excitation; Floquet theory 528 G.1 Floquet’s theorem 528 G.2 Example: Two states 530 G.3 Floquet theory and the RWA 531 G.4 Floquet theory and the Jaynes–Cummings model 531 G.5 Near-periodic excitation; adiabatic Floquet theory 532 G.6 Example: Two states 534 G.7 Adiabatic Floquet energy surfaces 536 Appendix H Transitions; spectroscopic parameters 537 H.1 Spectroscopic parameters 537 H.2 Relative transition strengths 538 References 542 Index 565 |
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