Physical realization of coupled Hilbert space mirrors for quantum state engineering

《Physical realization of coupled Hilbert space mirrors for quantum state engineering》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、JournalofModernOpticsVol.54,Nos.13–15,10Sep–15Oct2007,2237–2257PhysicalrealizationofcoupledHilbert-spacemirrorsforquantum-stateengineeringE.S.KYOSEVAy,N.V.VITANOV*yzandB.W.SHORE}ôyDepartmentofPhysics,SofiaUniversity,JamesBourchier5Blvd.,1164Sofia,BulgariazInstituteofSolidStatePhysics,Bulgarian

2、AcademyofSciences,Tsarigradskochausse´e72,1784Sofia,BulgariaxFachbereichPhysik,TechnischeUniversita¨tKaiserslautern,67653Kaiserslautern,Germany(Received12February2007;infinalform18March2007)Manipulationofsuperpositionsofdiscretequantumstateshasamathematicalcounterpartinthemotionofaunit-lengths

3、tatevectorinanN-dimensionalHilbertspace.Anysuchstatevectormotioncanberegardedasasuccessionoftwo-dimensionalrotations.Butthedesiredstatevectorchangecanalsobetreatedasasuccessionofreflections,thegeneralizationofHouseholdertransformations.InmultidimensionalHilbertspacesuchreflectionsequencesofferm

4、oreefficientproceduresforstatevectormanipulationthandosequencesofrotations.Wehereshowhowsuchreflectionscanbedesignedforasystemwithtwodegeneratelevels—ageneralizationofthetraditionaltwo-stateatom—thatallowstheconstructionofpropagatorsforangularmomentumstates.WeusetheMorris–Shoretransformationtoe

5、xpressthepropagatorintermsofMorris–ShorebasisstatesandCayley–Kleinparameters,whichallowsustoconnectpropertiesoflaserpulsestoHilbert-spacemotion.Undersuitableconditionsonthecouplingsandthecommondetuning,thepropagatorswithineachsetofdegeneratestatesrepresentproductsofgeneralizedHouseholderrefle

6、ctions,withorthogonalvectors.Weproposephysicalrealizationsofthisnovelgeometricalobjectwithresonant,near-resonantandfar-off-resonantlaserpulses.Wegiveseveralexamplesofimplementationsinrealatomsormolecules.1.IntroductionManipulationofdiscretequantumstateshaslongheldinterest,mostrecentlyforappli

7、cationtoquantuminformationprocessing[1].Inthesimplestrealizationsonedealswithanondegeneratetwo-statesystem(a‘two-levelatom’[2,3])andthroughpulsedresonantcoherentexcitationproducesaspecifiedsuperpositionofthetwostates,startingfromasinglestate.Followi