Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000010317706 | QC794.6.E9 S56 2011 | Open Access Book | Book | Searching... |
On Order
Summary
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 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.
Table of Contents
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 |