Manipulating Quantum Structures Using Laser Pulses

by Bruce W. Shore

• ISBN13: 9780521763578
• ISBN10: 0521763576
• Format: Hardcover
• Copyright: 2011-11-21
• Publisher: Cambridge University Press

Summary

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 Biography

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.

Table of Contents

Preface	p. xi
Acknowledgments	p. xiii
Introduction	p. 1
Objective	p. 1
Background	p. 1
Measurables, observables, and parameters	p. 2
Notation and nomenclature	p. 5
Limitations of the theory	p. 7
Basic references	p. 8
Atoms as structured particles	p. 9
Spectroscopy	p. 10
Quantum states	p. 13
Probabilities	p. 15
Radiation	p. 19
Thermal radiation; quanta	p. 19
Cavities	p. 20
Incoherent radiation	p. 21
Laser radiation	p. 22
Laser fields	p. 23
Field vectors	p. 31
Laser beams	p. 40
Photons	p. 41
Field restrictions	p. 43
The laser-atom interaction	p. 44
Individual atoms	p. 44
Detecting excitation	p. 50
The interaction energy; multipole moments	p. 52
Moving atoms	p. 54
Picturing quantum structure and changes	p. 57
Free electrons: Ponderomotive energy	p. 57
Picturing bound electrons	p. 58
The Lorentz force	p. 61
The wavefunction; orbitals	p. 62
The statevector; Hilbert spaces	p. 66
Two-state Hilbert spaces	p. 69
Time-dependent statevectors	p. 73
Picturing quantum transitions	p. 76
Incoherence: Rate equations	p. 78
Thermalized atoms; the Boltzmann equation	p. 78
The radiative rate equations	p. 79
The Einstein rates	p. 79
The two-state rate equations	p. 81
Solutions to the rate equations	p. 81
Comments	p. 83
Coherence: The Schrödinger equation	p. 85
Essential states; effective Hamiltonians	p. 87
The coupled differential equations	p. 88
Classes of interaction	p. 93
Classes of solutions	p. 93
The time-evolution matrix; transition probabilities	p. 95
Two-state coherent excitation	p. 97
The basic equations	p. 97
Abrupt start	p. 104
The rotating-wave approximation (RWA)	p. 108
Adiabatic time evolution	p. 118
Comparison of excitation methods	p. 135
Weak pulse: Perturbation theory	p. 137
Weak resonant excitation	p. 138
Pulse aftermath and frequency content	p. 138
Example: Excitation despite missing frequencies	p. 139
The Dirac (interaction) picture	p. 141
Weak broadband radiation; transition rates	p. 142
Fermi's famous Golden Rule	p. 144
The vector model	p. 146
The Feynman-Vernon-Hellwarth equations	p. 146
Coherence loss; relaxation	p. 150
Sequential pulses	p. 159
Contiguous pulses	p. 159
Pulse trains	p. 160
Examples	p. 162
Pulse pairs	p. 163
Vector picture of pulse pairs	p. 165
Creating dressed states	p. 167
Zero-area pulses	p. 168
Degeneracy	p. 171
Zeeman sublevels	p. 171
Radiation polarization and selection rules	p. 172
The RWA with degeneracy	p. 177
Optical pumping	p. 179
General angular momentum	p. 181
Three states	p. 186
Three-state linkages	p. 186
The three-state RWA	p. 188
Resonant chains	p. 197
Detuning	p. 201
Unequal Rabi frequencies	p. 211
Laser-induced continuum structure (LICS)	p. 218
Raman processes	p. 222
The Raman Hamiltonian	p. 222
Population transfer	p. 223
Explaining STIRAP	p. 230
Demonstrating STIRAP	p. 235
Optimizing STIRAP pulses	p. 237
Two-state versions of STIRAP	p. 239
Extending STIRAP	p. 243
Multilevel excitation	p. 253
Multiphoton and multiple-photon ionization	p. 253
Coherent excitation of JV-state systems	p. 255
Chains	p. 259
Branches	p. 277
Loops	p. 287
Multilevel adiabatic time evolution	p. 292
Averages and the statistical matrix (density matrix)	p. 299
Ensembles and expectation values	p. 299
Statistical averages	p. 300
Environmental averages	p. 302
Expectation values	p. 304
Uncertainty relations	p. 307
The density matrix	p. 308
Density matrix equation of motion	p. 313
Incorporating incoherent processes	p. 317
Rotating coordinates	p. 321
Multilevel generalizations	p. 324
Systems with parts	p. 331
Separability and factorization	p. 331
Center of mass motion	p. 333
Two parts	p. 338
Correlation and entanglement	p. 343
Preparing superpositions	p. 347
Superposition construction	p. 347
Nondegenerate states	p. 348
Degenerate discrete states	p. 350
Transferring superpositions	p. 351
State manipulations using Householder reflections	p. 352
Measuring superpositions	p. 357
General remarks	p. 357
Spin matrices and quantum tomography	p. 359
Two-state superpositions	p. 362
Analyzing multistate superpositions	p. 364
Analyzing three-state superpositions	p. 366
Alternative procedures	p. 368
Overall phase; interferometry and cyclic dynamics	p. 370
Hilbert-space rays	p. 371
Parallel transport	p. 372
Phase definition	p. 373
Michelson interferometry	p. 374
Alternative interferometry	p. 377
Ramsey interferometry	p. 378
Cyclic systems	p. 379
Atoms affecting fields	p. 387
Induced dipole moments; propagation	p. 387
Single field, N= 2	p. 389
Multiple fields	p. 402
Two or three fields, N = 3	p. 403
Four fields, N = 4; four-wave mixing	p. 410
Steady state; susceptibility	p. 413
Atoms in cavities	p. 419
The cavity	p. 420
Two-state atoms in a cavity	p. 423
Three-state atoms in a cavity	p. 429
Control and optimization	p. 435
Control theory	p. 435
Quantum control	p. 436
Optimization	p. 439
Angular momentum	p. 442
Angular momentum states	p. 442
Angular momentum coupling	p. 451
Hyperfine linkages	p. 456
The multipole interaction	p. 459
The bound-particle interaction	p. 459
The multipole moments	p. 462
Examples	p. 464
Induced moments	p. 464
Irreducible tensor form	p. 465
Rabi frequencies	p. 465
Angular momentum selection rules	p. 466
Classical radiation	p. 468
The Lorentz force; Maxwell's equations	p. 468
Wave equations	p. 470
Frequency components	p. 476
The influence of matter	p. 480
Pulse-mode expansions	p. 482
Quantized radiation	p. 487
Field quantization	p. 488
Mode fields	p. 496
Photon states	p. 505
The free-field radiation Hamiltonian	p. 507
Interpretation of photons	p. 509
Adiabatic states	p. 513
Terminology	p. 513
Adiabatic evolution	p. 515
The Dykhne-Davis-Pechukas (DDP) formula	p. 519
Dark states; the Morris-Shore transformation	p. 522
The Morris-Shore transformation	p. 522
Bright and dark states	p. 524
Fan linkages	p. 526
Chain linkages	p. 526
Generalizations	p. 527
Near-periodic excitation; Floquet theory	p. 528
Floquet's theorem	p. 528
Example: Two states	p. 530
Floquet theory and the RWA	p. 531
Floquet theory and the Jaynes-Cummings model	p. 531
Near-periodic excitation; adiabatic Floquet theory	p. 532
Example: Two states	p. 534
Adiabatic Floquet energy surfaces	p. 536
Transitions; spectroscopic parameters	p. 537
Spectroscopic parameters	p. 537
Relative transition strengths	p. 538
References	p. 542
Index	p. 565
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