Manipulating Quantum Structures Using Laser Pulses

588 Pages·2011·5.48 MB·english

by  Bruce W. Shore

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
theoryofsuchquantum-statemanipulationforresearchersandgraduatestudents.
Thebookprovidestheequations,andapproachesfortheirsolution,thatcanbeappliedto
complicatedmultilevelquantumsystems.Italsogivesthebackgroundtheoryforapplication
toisolatedatomsortrappedions,simplemolecules,andatomsembeddedinsolids.Partic-
ularattentionisgiventothewaysinwhichquantumchangescanbedisplayedgraphically
tohelpreadersunderstandhowquantumchangescanbecontrolled.
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,specializinginthetheoryoflaser-inducedatomic-vaporexcitation.
The present volume is part of an informal series of books all of which originated as
review articles published in Acta Physica Slovaca. The journal can be accessed for free
atwww.physics.sk/aps.
VladimirBuzek,editorofthejournal
MANIPULATING QUANTUM
STRUCTURES USING LASER PULSES
BRUCE W. SHORE
cambridge university press
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Firstpublished2011
PrintedintheUnitedKingdomattheUniversityPress,Cambridge
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Shore,BruceW.
Manipulatingquantumstructuresusinglaserpulses/BruceW.Shore.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-521-76357-8(hardback)
1. Nuclearexcitation. 2. Atomicstructure. 3. Coherentstates.
4. Perturbation(Quantumdynamics) 5. Laserinterferometry. I. Title.
QC794.6.E9S56 2011
(cid:1)
539.756–dc23 2011027979
ISBN978-0-521-76357-8Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceor
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Contents
Preface pagexi
Acknowledgments xiii
1 Introduction 1
1.1 Objective 1
1.2 Background 1
1.3 Measurables,observables,andparameters 2
1.4 Notationandnomenclature 5
1.5 Limitationsofthetheory 7
1.6 Basicreferences 8
2 Atomsasstructuredparticles 9
2.1 Spectroscopy 10
2.2 Quantumstates 13
2.3 Probabilities 15
3 Radiation 19
3.1 Thermalradiation;quanta 19
3.2 Cavities 20
3.3 Incoherentradiation 21
3.4 Laserradiation 22
3.5 Laserfields 23
3.6 Fieldvectors 31
3.7 Laserbeams 40
3.8 Photons 41
3.9 Fieldrestrictions 43
4 Thelaser–atominteraction 44
4.1 Individualatoms 44
4.2 Detectingexcitation 50
v
vi Contents
4.3 Theinteractionenergy;multipolemoments 52
4.4 Movingatoms 54
5 Picturingquantumstructureandchanges 57
5.1 Freeelectrons:Ponderomotiveenergy 57
5.2 Picturingboundelectrons 58
5.3 TheLorentzforce 61
5.4 Thewavefunction;orbitals 62
5.5 Thestatevector;Hilbertspaces 66
5.6 Two-stateHilbertspaces 69
5.7 Time-dependentstatevectors 73
5.8 Picturingquantumtransitions 76
6 Incoherence:Rateequations 78
6.1 Thermalizedatoms;theBoltzmannequation 78
6.2 Theradiativerateequations 79
6.3 TheEinsteinrates 79
6.4 Thetwo-staterateequations 81
6.5 Solutionstotherateequations 81
6.6 Comments 83
7 Coherence:TheSchrödingerequation 85
7.1 Essentialstates;effectiveHamiltonians 87
7.2 Thecoupleddifferentialequations 88
7.3 Classesofinteraction 93
7.4 Classesofsolutions 93
7.5 Thetime-evolutionmatrix;transitionprobabilities 95
8 Two-statecoherentexcitation 97
8.1 Thebasicequations 97
8.2 Abruptstart 104
8.3 Therotating-waveapproximation(RWA) 108
8.4 Adiabatictimeevolution 118
8.5 Comparisonofexcitationmethods 135
9 Weakpulse:Perturbationtheory 137
9.1 Weakresonantexcitation 138
9.2 Pulseaftermathandfrequencycontent 138
9.3 Example:Excitationdespitemissingfrequencies 139
9.4 TheDirac(interaction)picture 141
9.5 Weakbroadbandradiation;transitionrates 142
9.6 Fermi’sfamousGoldenRule 144
10 Thevectormodel 146
10.1 TheFeynman–Vernon–Hellwarthequations 146
10.2 Coherenceloss;relaxation 150
Contents vii
11 Sequentialpulses 159
11.1 Contiguouspulses 159
11.2 Pulsetrains 160
11.3 Examples 162
11.4 Pulsepairs 163
11.5 Vectorpictureofpulsepairs 165
11.6 Creatingdressedstates 167
11.7 Zero-areapulses 168
12 Degeneracy 171
12.1 Zeemansublevels 171
12.2 Radiationpolarizationandselectionrules 172
12.3 TheRWAwithdegeneracy 177
12.4 Opticalpumping 179
12.5 Generalangularmomentum 181
13 Threestates 186
13.1 Three-statelinkages 186
13.2 Thethree-stateRWA 188
13.3 Resonantchains 197
13.4 Detuning 201
13.5 UnequalRabifrequencies 211
13.6 Laser-inducedcontinuumstructure(LICS) 218
14 Ramanprocesses 222
14.1 TheRamanHamiltonian 222
14.2 Populationtransfer 223
14.3 ExplainingSTIRAP 230
14.4 DemonstratingSTIRAP 235
14.5 OptimizingSTIRAPpulses 237
14.6 Two-stateversionsofSTIRAP 239
14.7 ExtendingSTIRAP 243
15 Multilevelexcitation 253
15.1 Multiphotonandmultiple-photonionization 253
15.2 CoherentexcitationofN-statesystems 255
15.3 Chains 259
15.4 Branches 277
15.5 Loops 287
15.6 Multileveladiabatictimeevolution 292
16 Averagesandthestatisticalmatrix(densitymatrix) 299
16.1 Ensemblesandexpectationvalues 299
16.2 Statisticalaverages 300
16.3 Environmentalaverages 302
viii Contents
16.4 Expectationvalues 304
16.5 Uncertaintyrelations 307
16.6 Thedensitymatrix 308
16.7 Densitymatrixequationofmotion 313
16.8 Incorporatingincoherentprocesses 317
16.9 Rotatingcoordinates 321
16.10 Multilevelgeneralizations 324
17 Systemswithparts 331
17.1 Separabilityandfactorization 331
17.2 Centerofmassmotion 333
17.3 Twoparts 338
17.4 Correlationandentanglement 343
18 Preparingsuperpositions 347
18.1 Superpositionconstruction 347
18.2 Nondegeneratestates 348
18.3 Degeneratediscretestates 350
18.4 Transferringsuperpositions 351
18.5 StatemanipulationsusingHouseholder
reflections 352
19 Measuringsuperpositions 357
19.1 Generalremarks 357
19.2 Spinmatricesandquantumtomography 359
19.3 Two-statesuperpositions 362
19.4 Analyzingmultistatesuperpositions 364
19.5 Analyzingthree-statesuperpositions 366
19.6 Alternativeprocedures 368
20 Overallphase;interferometryandcyclicdynamics 370
20.1 Hilbert-spacerays 371
20.2 Paralleltransport 372
20.3 Phasedefinition 373
20.4 Michelsoninterferometry 374
20.5 Alternativeinterferometry 377
20.6 Ramseyinterferometry 378
20.7 Cyclicsystems 379
21 Atomsaffectingfields 387
21.1 Induceddipolemoments;propagation 387
21.2 Singlefield,N=2 389
21.3 Multiplefields 402
21.4 Twoorthreefields,N =3 403