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1、JournalofModernOpticsVol.54,Nos.13–15,10Sep–15Oct2007,2237–2257PhysicalrealizationofcoupledHilbert-spacemirrorsforquantum-stateengineeringE.S.KYOSEVAy,N.V.VITANOV*yzandB.W.SHORE}?yDepartmentofPhysics,So?aUniversity,JamesBourchier5Blvd.,1164So?a,BulgariazInstituteofSolidStatePhysics,Bulgarian
2、AcademyofSciences,Tsarigradskochausse′e72,1784So?a,BulgariaxFachbereichPhysik,TechnischeUniversita¨tKaiserslautern,67653Kaiserslautern,Germany(Received12February2007;in?nalform18March2007)Manipulationofsuperpositionsofdiscretequantumstateshasamathematicalcounterpartinthemotionofaunit-lengths
3、tatevectorinanN-dimensionalHilbertspace.Anysuchstatevectormotioncanberegardedasasuccessionoftwo-dimensionalrotations.Butthedesiredstatevectorchangecanalsobetreatedasasuccessionofre?ections,thegeneralizationofHouseholdertransformations.InmultidimensionalHilbertspacesuchre?ectionsequenceso?erm
4、oree?cientproceduresforstatevectormanipulationthandosequencesofrotations.Wehereshowhowsuchre?ectionscanbedesignedforasystemwithtwodegeneratelevels—ageneralizationofthetraditionaltwo-stateatom—thatallowstheconstructionofpropagatorsforangularmomentumstates.WeusetheMorris–Shoretransformationtoe
5、xpressthepropagatorintermsofMorris–ShorebasisstatesandCayley–Kleinparameters,whichallowsustoconnectpropertiesoflaserpulsestoHilbert-spacemotion.Undersuitableconditionsonthecouplingsandthecommondetuning,thepropagatorswithineachsetofdegeneratestatesrepresentproductsofgeneralizedHouseholderre?e
6、ctions,withorthogonalvectors.Weproposephysicalrealizationsofthisnovelgeometricalobjectwithresonant,near-resonantandfar-o?-resonantlaserpulses.Wegiveseveralexamplesofimplementationsinrealatomsormolecules.1.IntroductionManipulationofdiscretequantumstateshaslongheldinterest,mostrecentlyforappli
7、cationtoquantuminformationprocessing[1].Inthesimplestrealizationsonedealswithanondegeneratetwo-statesystem(a‘two-levelatom’[2,3])andthroughpulsedresonantcoherentexcitationproducesaspeci?edsuperpositionofthetwostates,startingfromasinglestate.Followi
