Manipulating quantum structures using laser pulses

The use of laser pulses to alter the internal quantum structure of individual atoms and molecules has applications in quantum information processing, the coherent control of chemical reactions and in quantum-state engineering. This book presents the underlying theory of such quantum-state manipulation for researchers and graduate students. The book provides the equations, and approaches for their solution, which can be applied to complicated multilevel quantum systems. It also gives the background theory for application to isolated atoms or trapped ions, simple molecules and atoms embedded in solids. Particular attention is given to the ways in which quantum changes can be displayed graphically to help readers understand how quantum changes can be controlled.

Author Notes

Bruce W. Shore worked as a theoretical physicist at the Lawrence Livermore National Laboratory for 30 years. His research dealt with numerical analysis and atomic physics, specializing in the theory of laser-induced atomic-vapor excitation.

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

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