We demonstrate a new technique for characterizing two-photon quantum states based on joint temporal correlation measurements using time resolved single photon detection by femtosecond upconversion. We measure for the first time the joint temporal density o

JointTemporalDensityMeasurementsforTwo-PhotonStateCharacterization

OnurKuzucu,1FrancoN.C.Wong,1SunaoKurimura,2andSergeyTovstonog2

1

ResearchLaboratoryofElectronics,MassachusettsInstituteofTechnology,Cambridge,Massachusetts02139,USA

2

NationalInstituteforMaterialsScience,1-1Namiki,Tsukuba-shi,Ibaraki305-0044,Japan

(Dated:July10,2008)

Wedemonstrateanewtechniqueforcharacterizingtwo-photonquantumstatesbasedonjointtemporalcorrelationmeasurementsusingtime-resolvedsingle-photondetectionbyfemtosecondup-conversion.Wemeasureforthe rsttimethejointtemporaldensityofatwo-photonentangledstate,showingclearlythetimeanti-correlationofthecoincident-frequencyentangledphotonpairgeneratedbyultrafastspontaneousparametricdown-conversionunderextendedphase-matchingconditions.Thenewtechniqueenablesustomanipulatethefrequencyentanglementbyvaryingthedown-conversionpumpbandwidthtoproduceanearlyunentangledtwo-photonstatethatisexpectedtoyieldaheraldedsingle-photonstatewithapurityof0.88.Thetime-domaincorrela-tiontechniquecomplementsexistingfrequency-domainmeasurementmethodsforamorecompletecharacterizationofphotonicentanglementinquantuminformationprocessing.

PACSnumbers:42.50.Dv,42.79.Nv,42.50.Ar,42.65.Lm

arXiv:0807.1573v1 [quant-ph] 10 Jul 2008

Spontaneousparametricdown-conversion(SPDC)isapowerfulmethodforgeneratingtwo-photonstatesforquantuminformationprocessing(QIP).Thejointquan-tumstatecanbeengineeredforspeci cQIPapplicationsbytailoringitspolarization,momentum,andspectralde-greesoffreedom.Ultrafast-pumpedSPDCisofgreatinterestbecauseawellde nedtimeofemissionisdesir-ableinclockedapplicationssuchaslinearopticsquan-tumcomputing(LOQC)[1].InultrafastSPDC,spectralengineeringofthetwo-photonstatecanbeaccomplishedbymanipulatingthecrystalphase-matchingfunctionandthepumpspectralamplitudetoyielduniqueformsoftwo-photonfrequencyentanglement.Forexample,coincident-frequencyentanglementwithstrongpositivecorrelationbetweensignalandidleremissionfrequenciescanbeusedtoimprovetime-of- ightmeasurementsbe-yondthestandardquantumlimit5].Ontheotherhand,onecanutilizeatwo-photonstatewithnegligiblespectralcorrelationstoimplementaheraldedsourceofpure-statesinglephotons,whichcanbeavaluablere-sourceforLOQC[6,7].

Characterizingthespectralcorrelationsofatwo-photonstatecanbedonebymeasuringthejointspectraldensity(JSD)pro lewithtunablenarrowband lteringofthesignalandidler[6,7,8].Hong-Ou-Mandelquan-tuminterference[9]isalsousefulforquantifyingthetwo-photoncoherencebandwidthandtheindistinguishabil-ityofthephotonpair.However,thetwomeasurementsdonotgivethewholepictureofthetwo-photonstate.Bothmeasurementsareinsensitivetothespectralphaseandthereforecannotcapturethetime-domaindynamicsunlessthejointstateisknowntobetransformlimited.Moreover,JSDmeasurementsinwavelengthregionswithlowdetectore ciencyorhighdetectornoisecanbechal-lengingduetolongacquisitiontimesandlowsignal-to-noiseratios.Frequency-domaintechniquesforestimat-ingthespectralphaseexist,buttheyarenotsimpleto

implementinpracticeInultrafastopticsultrashortpulsesareroutinelyana-lyzedspectrallyandtemporally,buttime-domaincharac-terizationtoolsarenoteasytoimplementforsinglepho-tons.Recentlywehaveintroducedatime-resolvedsingle-photonmeasurementtechniquebyuseoffemtosecondupconversion[11].InthisLetterweutilizethissingle-photontime-domaincharacterizationmethodtomeasureforthe rsttimethejointtemporaldensity(JTD)pro- leofatwo-photonquantumstate.Inparticular,wemeasureddirectlythetimecorrelationsofsignal-idlerar-rivaltimesofultrafastpumpedSPDCunderextendedphasematchingconditionsshowingclearlythatthecoincident-frequencyentangledphotonsweretimeanti-correlated.Furthermore,byvaryingtheSPDCpumpspectrum,wewereabletomanipulatethetemporalcor-relationsofthesignalandidler,andobtainanearlyun-entangled(temporally)two-photonstate.Thisnewtech-niquecanbeusedinconjunctionwithfrequency-domainmethodstoprovideamorecompletecharacterizationofsingleandentangledphotons.

Toproperlyde neJTD,we rstexpressthetwo-photonstateintime-domainvariables|Ψ =

dτSdτIA(τS,τI)|τS |τI ,wherethesingle-photonFockstateisde nedas|τj ≡a (τj)|0 ,forj=S,I.Thetem-poralcorrelationsofthesignalandidleraredeterminedbythejointtemporalamplitude,A(τS,τI),andwede-2

netheassociatedprobabilitydensity,(|A(τS,τI)|),asthejointtemporaldensity.Analogoustothefrequency-domainmethods,theJTDcanbemeasuredbyusingnarrowbandtemporal lteringandcoincidencedetection.FortypicalultrafastSPDCexperiments,timingreso-lutionof～100fsisneededformeasuringarrivaltimesofsinglephotons.Currentsingle-photondetectorswithtensofpicosecondstimingresolutionarenotsuitableforthispurpose.Forthetwo-photonJTDmeasurement,weappliedourrecentlydevelopedtime-resolvedsingle-