Multipartite entangled states in coupled quantum dots and ca

We investigate the generation of multipartite entangled state in a system of N quantum dots embedded in a microcavity and examine the emergence of genuine multipartite entanglement by three different characterizations of entanglement. At certain times of d

Multipartiteentangledstatesincoupledquantumdotsandcavity-QED

XiaoguangWang1,2,MangFeng2,andBarryCSanders1

1.DepartmentofPhysicsandCentreforAdvancedComputing–AlgorithmsandCryptography,

MacquarieUniversity,Sydney,NewSouthWales2109,Australia

2.InstituteforScienti cInterchange(ISI)Foundation,

VialeSettimioSevero65,I-10133Torino,Italy

(February1,2008)WeinvestigatethegenerationofmultipartiteentangledstateinasystemofNquantumdotsembeddedinamicrocavityandexaminetheemergenceofgenuinemultipartiteentanglementbythreedi erentcharacterizationsofentanglement.AtcertaintimesofdynamicalevolutiononecangeneratemultipartiteentangledcoherentexcitonstatesormultiqubitWstatesbyinitiallypreparingthecavity eldinasuperpositionofcoherentstatesortheFockstatewithonephoton,respectively.Finallywestudyenvironmentale ectsonmultipartiteentanglementgenerationand ndthatthedecayratefortheentanglementisproportionaltothenumberofexcitons.PACSnumbers03.65.Ud,68.65.Hb

I.INTRODUCTION

arXiv:quant-ph/0212034v1 6 Dec 2002

Quantuminformationprocessingo ersimportantca-pabilitiesforquantumcommunicationsandquantumcomputationinavarietyofphysicalsystems,andthesolid-stateimplementationisoneofthemostpromis-ingcandidates.Semiconductorquantumdots(QDs)areappealingfortherealizationofquantumcomputerandquantuminformationprocessing.Spatialcon nementofexcitonsinthreedimensionsleadstodiscreteenergylev-els,andthemaincausesofphasedecoherence,namelyscatteringevents,arehighlysuppressed[1].Inthisre-spect,QDsareverypromisingcomparedtoothersemi-conductorstructureswithbandstates.Moreoveraquan-tumcomputerschemebasedonquantumdotarraysisscalableupto≥100qubits.

Entanglementisaessentialsourceforquantumcom-putingandquantuminformationprocessing.Itiswell-knownthatacontrolled-NOTgatecangenerateamax-imallyentangledstate.Variousschemesfortherealiza-tionofcontrolled-NOTgatesinQDsareproposedwitheithertheelectronspinorthediscreteelec-tronicchargedegreeoffreedomasqubits[6,7,8].Forexample,Imamo¯gluetal.[4]proposedaschemethatre-ijalizedacontrolled-NOTgateCNOTbetweentwodistantquantumdotsiandjviathecavityquantumelectro-magneticdynamics(CQED)techniques.Herethe rst

ij

superscriptiinCNOTdenotesthecontrolandtheseconddenotesthetarget.Thesecontrolled-NOTgatesinturncanbeusedtogenerateatripartitemaximallyentangledGreenberger-Horne-Zeilinger(GHZ)stateas|0 |0

1312

|0 +|1 |1 |1 =CNOTCNOT(|0 +|1 ) |0 |0 .Quirogaetal.showedthatanopticallycontrolledex-citontransferprocesscangeneratemaximallyentangledBellstatesandGHZstates.Todemonstratethatexcitonsincoupledquantumdotsareidealcandidatesforreliablepreparationofentangledstatesinsolid-statesystems,Chenetal.[12]experimentallyinvestigatedhowtoopticallyinduceentanglementofexcitonsinasinglegalliumarsenideQD:theentanglementisidenti edby

thespectrumofthephase-sensitivehomodyne-detectedcoherentnonlinearopticalresponse.

Althoughnoexperimentalobservationofentanglementofmany-excitonsystemshasyetoccurred,thetheoreti-calstudiesarenecessaryifwedesiretohavealarge-scalequantumcomputingdevice.InarecentinvestigationbyLiuetal[13]forgeneratingbipartiteentangledcoherentexcitonstatesinasystemoftwocoupledquantumdotsandCQEDwithdiluteexcitons,theyfoundthatthebi-partitemaximallyentangledcoherentexcitonstatescanbegeneratedwhentheinitialcavity eldisinanoddcoherentstate.Therelationbetweenentanglementofexcitonandphotonnumbersinthecavitywasalsodis-cussed.

Itisinterestingtoextendtomultipartiteentanglementinsuchsystems.Multipartiteentanglementisnotonlyofintrinsicinterestitselfbutalsoofpracticalimportanceinquantuminformationproposalssuchasquantumtele-portationandquantumcryptography.OnemotivationtoconsidermultipartiteentanglementinmanyQDsisthataround10QDscanbeembeddedinamicrodiskstruc-tureandcoupledtoasinglecavitymodeinthequantuminformationprocessschemeproposedbyImamo¯gluetal.Wewill rstextendthemodelofRef.[11]tothecaseofmanyQDs,andthenstudyhowtogeneratemultipartiteentangledstatesandexaminemultipartiteentanglementinsuchsystems.

Thepaperisorganizedasfollows.InSec.II,wepresentamodelforcoupledQDsinCQEDanddeterminetheex-actstatevectoratanytimet,whichwillbeshowntobeamultipartiteentangledstateinsometimeranges.InSec.III,weusethreedi erentmethodstoexaminethemultipartiteentanglementinthestate.TheninSec.IV,weshowthatmultipartiteentangledcoherentexcitonstatescanbegeneratedatcertaintimesduringthedy-namicalevolution.InSec.V,weanalysethee ectsofenvironmentonthegenerationofmultipartiteentangle-ment.TheconclusionsaregiveninSec.VI.

We investigate the generation of multipartite entangled state in a system of N quantum dots embedded in a microcavity and examine the emergence of genuine multipartite entanglement by three different characterizations of entanglement. At certain times of d

II.MULTIPARTITEENTANGLEDSTATES

Weconsiderquantumdotsembeddedinasingle-modecavity.WeassumethattheQDsaresu cientlylargeandthereareonlyafewelectronsexcitedfromvalenceband

to

conduction

band

[13].

Intheassumptionoflowexci-tonexcitationdensity,excitonoperatorscanbeapprox-imatedbybosonoperators,andallnonlineardynamicssuchasexciton-excitoninteractioncanbeneglected.Asthedistancebetweenanytwoexcitonsisalsoassumedtobelarge,theinteractionbetweenanytwoexcitonscanbesafelyneglected.Thereexistsaresonantinteractionbetweentheexcitonsandthecavity eld.TheHamilto-nianundertherotatingwaveapproximationisgivenby(¯h=1)[13,14]

H=

ωb 0b0

+ω

N

b nbn

+

n=1n=1

N

gn(b nb0+b0bn),

(1)

whereb 0(b0)isthecreation(annihilation)operatorof

thecavity eldwithfrequencyω,b n(bn)(n=1,2,···,N)denot …… 此处隐藏：17130字，全部文档内容请下载后查看。喜欢就下载吧 ……