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ElementsofQuantumInformation Editedby WolfgangP.Schleichand HerbertWalther 1807–2007 Knowledge for Generations Each generation has its unique needs and aspirations. When Charles Wiley first openedhis small printing shop in lower Manhattan in 1807, it was a generation of boundless potential searching for an identity. And we were there, helping to define a new American literary tradition. Over half a century later, in the midst of the Second Industrial Revolution, it was a generation focused on building the future. Onceagain, we werethere, supplying the criticalscientific,technical, and engineering knowledge that helped frame the world. Throughout the 20th Century, and into the new millennium, nations began to reach out beyond their own bordersand a new international community was born.Wiley was there, ex- panding its operations around the world to enable a global exchange of ideas, opinions,and know-how. For 200 years, Wiley has been an integral part of each generation’s journey, enabling the flow of information and understanding necessary to meet their needs and fulfill their aspirations. Today, bold new technologies are changing the way we live and learn. Wiley will be there, providing you the must-have knowledge you need to imagine new worlds, new possibilities, and new oppor- tunities. Generations come and go, but you can always count on Wiley to provide you the knowledge you need,when and whereyou need it! WilliamJ. Pesce PeterBooth Wiley Presidentand Chief ExecutiveOfficer Chairman of the Board Elements of Quantum Information Edited by Wolfgang P. Schleich and Herbert Walther TheEditors AllbookspublishedbyWiley-VCHarecarefully produced.Nevertheless,editors,authorsand Prof.Dr.WolfgangP.Schleich publisherdonotwarranttheinformationcontained UniversitätUlm inthesebookstobefreeoferrors.Readersare Abteilungf.Quantenphysik advisedtokeepinmindthatstatements,data, Albert-Einstein-Allee11 illustrations,proceduraldetailsorotheritemsmay 89069Ulm inadvertentlybeinaccurate. Germany LibraryofCongressCardNo.: appliedfor Prof.Dr.HerbertWalther† MPIfürQuantenoptik BritishLibraryCataloguing-in-Publication Hans-Kopfermann-Str.1 Data: 85748Garching Acataloguerecordforthisbookisavailablefrom Germany theBritishLibrary. Bibliographicinformationpublishedby theDeutscheBibliothek TheDeutscheBibliothekliststhispublicationinthe CoverImage DeutscheNationalbibliografie;detailed SegmentedlinearPaultrap,Universityof bibliographicdataisavailableintheInternetat Ulm,Germany(2006)byS.Schulzand http://dnb.d-nb.de F.Schmidt-Kaler. Thetrapisfabricatedfromgoldcoated (cid:2)c 2007WILEY-VCHVerlagGmbH&CoKGaA, ceramicwaferswhicharestructuredby Weinheim fs-laserpulses.Thelargenumberof12 segmentsinthe500μmwideloadingzone Allrightsreserved(includingthoseoftranslation –attherighthandsideoftheslit–and19 intootherlanguages).Nopartofthisbookmaybe segmentsinthe250μmwideprocessor reproducedinanyform–byphotocopying, zoneofthistrappingdeviceallowto microfilm,oranyothermeans–nortransmittedor scale-upquantumcomputingwithtrapped translatedintoamachinelanguagewithoutwritten ions. permissionfromthepublishers.Registered ThearticleOptimizationofSegmented names,trademarks,etc.usedinthisbook,even LinearPaulTrapsandTransportofStored whennotspecificallymarkedassuch,arenotto ParticlesbyS.Schulz,U.Poschinger, beconsideredunprotectedbylaw. K.Singer,andF.Schmidt-Kalerexplains howtotransportionsinthisdevicefastbut PrintedintheFederalRepublicofGermany withoutanyheatingeffects. Printedonacid-freepaper Composition:SteingraeberSatztechnikGmbH, Ladenburg Printing:StraussGmbH,Mörlenbach Bookbinding: Litges&DopfBuchbinderei GmbH,Heppenheim ISBN:978-3-527-40725-5 V Contents PrefacetotheBook XVII PrefacetotheJournal XIX ListofContributors XXI 1 TheDeterministicGenerationofPhotons byCavityQuantumElectrodynamics 1 H.Walther 1.1 Introduction 1 1.2 OscillatoryExchangeofPhotonsBetweenanAtomandaCavity Field 1 1.2.1 ExperimentalSet-upoftheOne-atomMaser 3 1.2.2 One-atomMaserasaSourceofNon-classicalLight 5 1.2.3 ReviewofExperimentsonBasicPropertiesoftheOne-atom Maser 8 1.2.4 StatisticsofDetectorClicks 12 1.2.5 TrappingStates 13 1.2.6 TrappingStateStabilization 17 1.2.7 FockStatesonDemand 17 n 1.2.8 DynamicalPreparationof -photonStatesinaCavity 18 1.2.9 TheOne-atomMaserSpectrum 24 1.3 OtherMicrowaveCavityExperiments 26 1.3.1 Collapse-and-revivaloftheRabiOscillationsinanInjected CoherentField 26 1.3.2 Atom-photonandAtom-atomEntanglement 27 1.3.3 Atom-photonPhaseGate 28 1.3.4 QuantumNondestructive-measurementofaPhoton 28 1.3.5 Wigner-functionofaOne-photonState 29 1.3.6 MultiparticleEntanglement 29 1.3.7 SchrödingerCatsandDecoherence 29 VI Contents 1.4 CavityQEDExperimentsintheVisibleSpectralRegion 30 1.4.1 TheOne-atomLaser 30 1.4.2 AtomsPushedbyaFewPhotons 31 1.4.3 Single-photonSources 33 1.4.4 Single-atomLaserusinganIonTrap 34 1.5 ConclusionsandOutlook 38 References 39 2 OptimizationofSegmentedLinearPaulTraps andTransportofStoredParticles 45 StephanSchulz,UlrichPoschinger,KilianSinger,and FerdinandSchmidt-Kaler 2.1 Introduction 45 2.2 OptimizationofaTwo-layerMicrostructuredIonTrap 46 2.2.1 DesignObjectives 47 2.2.2 OperatingModeandModelingoftheSegmentedLinearPaul Trap 49 2.2.3 OptimizationoftheRadialPotential 51 2.2.4 OptimizationoftheAxialPotential 52 2.3 OpenLoopControlofIonTransport 54 2.3.1 Non-adiabaticHeatingSources 54 2.3.2 OverviewoftheAppliedOptimizationStrategies 55 2.3.3 TheOptimalControlMethod 55 2.3.4 OptimizationResults 58 2.3.5 IonHeatingduetoAnharmonicDispersion 59 2.3.6 QuantumMechanicalEstimateofNon-adiabaticParametric Heating 59 2.3.7 ImprovedInitialGuessFunctionandUltra-fastTransport 60 2.3.8 DiscussionoftheOpen-loopResult 62 2.4 Outlook 64 A Appendix 65 References 66 3 TransportDynamicsofSingleIonsinSegmented MicrostructuredPaulTrapArrays 69 R.Reichle,D.Leibfried,R.B.Blakestad,J.Britton,J.D.Jost,E.Knill, C.Langer,R.Ozeri,S.Seidelin,andD.J.Wineland 3.1 Introduction 69 3.2 ClassicalEquationsofMotion 71 3.3 ClassicalDynamicsofIonTransport 72 3.3.1 HomogeneousSolution 73 3.3.2 Green’sFunctionandGeneralSolution 74 Contents VII 3.3.3 AdiabaticLimit 75 3.4 QuantumandClassical,DraggedHarmonicOscillators withConstantFrequency 76 3.5 TheDraggedQuantumHarmonicOscillator 78 3.6 TransportDynamicsinaWell-controlledRegime 81 3.6.1 TwoAnalyticalExamples 82 3.6.2 Near-optimumTransportFunctions 86 3.6.3 High-frequencyLimit,AdiabaticTransport,andApproximate Trajectories 86 3.7 Pleasesupplyashorttitle 87 3.7.1 DeterminationofWaveforms 87 3.7.2 PotentialFluctuationsandAspect-ratioRule 90 3.8 Conclusions 95 A Appendix 96 References 96 4 EnsembleQuantumComputationandAlgorithmicCooling inOpticalLattices 99 M.Popp,K.G.H.Vollbrecht,andJ.I.Cirac 4.1 Introduction 99 4.2 PhysicalSystem 102 4.2.1 Bose-HubbardModel 102 4.2.2 InitialStateProperties 103 4.2.3 EntropyasFigureofMerit 105 4.2.4 BasicOperations 106 4.3 EnsembleQuantumComputation 108 4.4 CoolingwithFiltering 112 4.5 AlgorithmicGroundStateCooling 114 4.5.1 TheProtocol 114 4.5.2 TheoreticalDescription 115 4.6 Conclusion 118 References 119 5 QuantumInformationProcessinginOpticalLattices andMagneticMicrotraps 121 PhilippTreutlein,TiloSteinmetz,YvesColombe,BenjaminLev,Peter Hommelhoff,JakobReichel,MarkusGreiner,OlafMandel,ArturWidera, TimRom,ImmanuelBloch,andTheodorW.Hänsch 5.1 Introduction 121 5.2 OpticalLattices 122 5.2.1 PreparationofaQubitRegister 122 5.2.2 AQuantumConveyerBeltforNeutralAtoms 123 VIII Contents 5.2.3 ControlledCollisions 124 5.3 MagneticMicrotraps 127 5.3.1 QubitStatesontheAtomChip 128 5.3.2 State-dependentMicrowavePotentials 132 5.3.3 QubitReadoutinMicrotraps 135 5.3.3.1 StablefiberFabry-PerotCavities 137 5.3.3.2 FFPCavityFabricationandPerformance 137 5.3.4 On-chipAtomDetectionwithaFFPCavity 138 5.3.5 SingleAtomPreparation 141 5.4 Conclusion 142 References 142 6 Two-dimensionalBose-EinsteinCondensates inaCO -laserOpticalLattice 145 2 GiovanniCennini,CarstenGeckeler,GunnarRitt,TobiasSalger,and MartinWeitz 6.1 Introduction 145 6.2 ExperimentalSetupandProcedure 146 6.3 ExperimentalResults 148 6.4 Conclusions 151 References 153 7 CreatingandProbingLong-rangeOrderinAtomicClouds 155 C.vonCube,S.Slama,M.Kohler,C.Zimmermann,and Ph.W.Courteille 7.1 Introduction 155 7.2 CollectiveCoupling 157 7.2.1 ExperimentalSetup 158 7.2.1.1 RingCavity 159 7.2.1.2 DipoleTrapfor85Rb 160 7.2.1.3 OpticalMolasses 162 7.2.2 SignaturesofCollectiveAtomicRecoilLasing 163 7.2.2.1 BeatNoteofFieldModes 163 7.2.2.2 SpectraofRecoil-inducedResonances 165 7.2.2.3 AtomicTransport 166 7.3 CreatingLong-rangeOrder 168 7.3.1 AnalyticTreatmentforPerfectBunching 168 7.3.1.1 RadiationPressure 170 7.3.1.2 Phase-lockingbyImperfectMirrors 171 7.3.2 SimulationsofAtomicTrajectorieswithFrictionandDiffusion 172 7.3.2.1 LasingThreshold 173 7.3.2.2 Self-synchronization 174 Contents IX 7.4 ProbingLong-rangeOrder 176 7.4.1 BraggScattering 176 7.4.2 HeterodynedBraggSpectra 178 7.4.3 MeasuringtheBraggScatteringPhase 179 7.5 Conclusion 180 References 181 8 DetectingNeutralAtomsonanAtomChip 185 MarcoWilzbach,AlbrechtHaase,MichaelSchwarz,DennisHeine,Kai Wicker,XiyuanLiu,Karl-HeinzBrenner,SönkeGroth,ThomasFernholz, BjörnHessmo,andJörgSchmiedmayer 8.1 Introduction 185 8.2 DetectingSingleAtoms 186 8.2.1 MeasuringtheScatteredLight: FluorescenceDetection 186 8.2.2 MeasuringtheDrivingField 187 8.2.2.1 AbsorptiononResonance 187 8.2.2.2 Refraction 189 8.2.3 Cavities 189 8.2.3.1 AbsorptiononResonance 189 8.2.3.2 Refraction 190 8.2.3.3 ManyAtomsinaCavity 190 8.2.4 ConcentricCavity 191 8.2.5 Miniaturization 191 8.3 PropertiesofFiberCavities 192 8.3.1 LossMechanismsforaCavity 193 8.3.2 LossesduetotheGapLength 194 8.3.3 LossesduetoTransversalMisalignment 195 8.3.4 LossesduetoAngularMisalignment 196 8.3.5 FresnelReflections 197 8.4 OtherFiberOpticalComponentsfortheAtomChip 199 8.4.1 FluorescenceandAbsorptionDetectors 199 8.4.2 ASingleModeTaperedLensedFiberDipoleTrap 199 8.5 IntegrationofFibersontheAtomChip 201 8.5.1 BuildingFiberCavities 201 8.5.2 TheSU-8Resist 203 8.5.3 TestoftheSU-8Structure 204 8.6 PilotTestforAtomDetectionwithSmallWaists 205 8.6.1 DroppingAtomsthroughaConcentricCavity 205 8.6.2 DetectingMagneticallyGuidedAtoms 207 8.7 Conclusion 208 References 209