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

histograms.Astheupconversionpulsewasscannedthroughthearrivalwindowsofbothphotons,theonlyin-stancewherethetwoupconverterscouldsimultaneouslydetectphotonswasaroundthetimeorigin.Foranup-conversionpumppowerof580mW,the

internalconver-sione ciencywasestimatedtobe25%[11].However,theupconversionprobabilityperpumppulsewasactu-allylowerbecausethepumppulsewasmuchshorterthanthee ectivepulsewidthofthesignalandidler.Inordertomanipulatethejointtemporalamplitudewithouta ectingtheupconversiontimingperformance,wemodi edonlytheSPDCpumpbandwidthbyin-sertinga lterfromasetofinterference lters(3-dBbandwidths:3.6nm,2.1nm,and1.1nm)beforethePP-KTPcrystal.Themeasurednormalizedcoincidencehis-togramsfordi erentSPDCpumpbandwidthsareplot-tedinFig.3.AstheSPDCpumpbandwidthwasre-duced,thesingle-photoncoherencetimeincreasedandconsequentlythecoincidencepeaksbecamewider.Inthesame gure,wealsoshowthetheoreticalpredictionsforthecoincidencehistogramsthatwecalculatebasedonthejointtemporalamplitudewitha nite-durationupconversionpumppulse.Theparametersforthecalcu-lationaretheupconversionanddownconversionpumpbandwidthsandthetwo-photoncoherencebandwidththatwemeasuredwiththeHOMinterference[4].Weassumea atspectralphasepro leinourjointtempo-ralamplitudecalculationleadingtopredictedtemporalcoincidencepro lesthatsuggesttransform-limitedtwo-photonstates.ThegoodagreementinFig.3betweendataandtheoryindicatesthattheSPDCoutputpho-tonpairswereindeedclosetothetransformlimit.Thisobservationisonlypossiblewithtime-domainmeasure-mentsbecausefrequency-domainmethodswouldbein-sensitivetodispersivebroadeningofthephotons.

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FIG.3:(Coloronline)NormalizedcoincidencehistogramsforvariousSPDCpump3-dBbandwidths:(6-,3.6-,2.2-,and1.1-nm).Theoreticalcoincidencepro lesareplottedasdashedlines.

3

Thetime-resolvedupconversionmethodenabledustomeasurethejointtemporaldensitybyvaryingthesig-nalandidlerrelativedelaysindependently.Wesettheupconversionpumpbandwidthto～6nm,andwemadetheJTDmeasurementsusingoneofthefourSPDCpumpbandwidths.Thecoincidencecountswererecordedoveratwo-dimensionaltimegridwith60-saveragingforeachdatapoint.ForallSPDCpumpbandwidthsex-cept1.1nm,thegridsizeforthetimedelayswassetto2ps×2ps(witha133fsstepsize).Weincreasedthegridsizeto4ps×4ps(266fsstepsize)forthe1.1nmpumpbandwidth.ThenormalizedcoincidencedataforallSPDCpumpbandwidthsareshownassurfaceplotsoverthetwo-dimensionaltimegridsinFig.4(a)-(d).WeseedramaticchangesintheJTDpro lewithachangeoftheSPDCpumpbandwidth.Witha6nmSPDCpumpbandwidththeJTDcoincidencepro leclearlyexhibitstimeanti-correlationthatisindicativeoftwo-photoncoincident-frequencyentanglement[4].Withsmallerpumpbandwidths,theJTDdistributionsbecomemoresymmetric,whichcorrespondstoreducedtemporalandspectralcorrelations.

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FIG.4:(Coloronline)Experimentaljointtemporaldensitiesforvariousdownconversionpump3-dBbandwidths:(a)6nm,(b)3.6nm,(c)2.2nm,(d)1.1nm.

Wecanquantifythetwo-photonfrequencyentangle-mentasafunctionofthepumpbandwidthbasedonthemeasuredJTDdistributionsandbyusingSchmidtde-compositionforcontinuousvariables[12].Inthisformal-ism,thejointtemporalamplitude,A(τs,τi),isexpressedasadiscretesumofthetemporaleigenmodeswitheigen-valuesλn,throughwhichtheentanglemententropybecomputedasS= n

cank=1λklog2λk[12].Figure5showsthecomputedentanglemententropyfromtheex-perimentalJTDdistributionsinFig.4assumingthatthejointstateistransformlimited.Forcomparison,wehave