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

alsocalculatedthetheoreticalentropycurvesasafunc-tionoftheSPDCpumpbandwidth,wherethepumpspectrumis

assumedtobeGaussian.TwocurvesareplottedinFig.5,onerepresentingaGaussianandtheotherasincphase-matchingfunction.ForaGaussianphase-matchingfunction,afullyfactorizabletwo-photonstateispredictedwithapumpbandwidthof～1.2nm,andyieldinganentropyofzero.Forthemorerealis-ticsincfunctionforthephasematching,ahighlybutnotcompletelyfactorizabletwo-photonstateisachiev-able.Sincethesinc-typespectralresponsecorrespondstoaboxcarshapeinthetimedomain,itnecessitatestheinclusionofhigherorderSchmidtmodesandhenceincreasestheentanglemententropy.

Figure5showsagoodqualitativeagreementbetweenthetheoreticalentropycurvesandtheentropyvaluesobtainedfromtheJTDdistributions.Theentangle-mententropycorrespondingtotheexperimentalJTDpro lesarelowerthanthetheoreticalcurveforthesincphase-matchingfunction.Thisisreasonableifwetakeintoaccountthattheactualtime-domainpro leofthephase-matchingfunctionissmootherthanaboxcarshapebecauseofgratinginhomogeneity,ascon rmedbythesingleshistogrammeasurementsofFig.2.Therefore,theexperimentalJTDdistributionscanbeexpressedwithasmallernumberofSchmidtmodes,resultinginalowerentanglemententropythanthatofthetheo-reticalofasincfunction.Fora1.1-nmSPDCpumpbandwidth,whichyieldsanoutputthatisnearlyfac-torizable,wehavecomputedthepurityoftheheraldedsingle-photonstate=Tr( ρS)= ∞as～0.88,wherepurityisde nedasp2

2

n=0λn[6,12].Thispurityvaluecom-pareswellwiththatofthepure-statesinglephotonsgen-eratedunderSPDCusingadi erentspectralengineeringmethod[7].Webelievethatthepuritycanbefurtherimprovedby nercontroloverthepumpbandwidthandadditionalspectral ltering.Incomparison,theoutputforthecaseofa6-nmSPDCpumpbandwidthyieldsapurityof～0.38,whichisaconsequenceofthehighdegreeofcoincident-frequencyentanglement.

Inconclusion,wehavedevelopedatime-domainmeasurementtechniqueforsinglephotonswithsub-picosecondresolutionthatweusedtomeasurethetwo-photonjointtemporaldensityforthe rsttime.Weappliedthetechniquetoverifyanti-correlationinthearrivaltimesofthesignalandidlerphotonsthatwerecoincident-frequencyentangled.Finally,thenewtoolal-lowedustomonitorthee ectofvaryingtheSPDCpumpbandwidths,leadingtothegenerationofanearlyfactor-izabletwo-photonstate,whichshouldbeofinteresttomanyquantuminformationprocessingapplications.WebelievethattheJTDmeasurementtechniqueisapow-erfultoolforengineeringtemporalandspectralcorrela-tionsofultrafastSPDCphotons.Suchacharacteriza-tiontechniquewouldcomplementthefrequency-domain

4

counterpartstoquantifyandmanipulatemulti-photon

y

portnE tnem

elgnatnE012345678

Pump bandwidth [nm]

FIG.5:(Coloronline)Entanglemententropyvaluescalcu-latedfromexperimentalJTDdistributionsforvariousSPDCpumpbandwidthsofFig.4.Thetheoreticalentropyvaria-tionsforGaussian(black)andsinc-type(red)phase-matchingfunctionsaregiveninsolidcurves.

entanglementforquantuminformationprocessingappli-cations.

ThisworkwassupportedinpartbytheHewlett-PackardLaboratoriesandbytheNationalInstituteofInformationandCommunicationsTechnology,Japan.

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