A Frequency-Multiplexed Coherent Electro-Optic Memory in Rare Earth Doped Nanoparticles - Fossati et al. - Unknown - Unknown

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AFrequency-MultiplexedCoherentElectro-OpticMemoryinRareEarthDopedNanoparticlesAlexandreFossati,yShupingLiu,y,zJennyKarlsson,yAkioIkesue,{AlexandreTallaire,yAlbanFerrier,y,xDianaSerrano,yandPhilippeGoldner,yyChimieParisTech,PSLUniversity,CNRS,InstitutdeRecherchedeChimieParis,F-75005Paris,FrancezShenzhenInstituteforQuantumScienceandEngineering,SouthernUniversityofScienceandTechnology,518055Shenzhen,China{WorldLaboratory,Mutsuno,Atsuta-ku,Nagoya456-0023,JapanxSorbonneUniversite,FacultedesSciencesetIngenierie,UFR933,F-75005Paris,FranceE-mail:philippe.goldner@chimieparistech.psl.euSupportingInformationAvailableExperimentalEu3+:YOnanoparticleswereobtainedbyhomogeneousprecipitationandhightempera-23tureairannealingmethods,asdescribedindetailsinRefs.1,2Yttriumhydroxycarbonateamorphousprecipitatesweresynthesizedfromamixtureofwater,ureaandmetalnitrates,whileyttriumoxideparticleswiththecubicphasewereobtainedfollowingatwo-stepairannealingat800and1200C.Thisprocedureleadstowelldispersedandsingle-crystallineparticles.Opticalcoherencelifetimesarefurtherextendedbytreatmentunderhigh-poweroxygenplasmaforafewminutes.21

1OpticalexcitationofEu3+7F!5Dtransitionat580.8830nm(vac.)wasprovidedbya00frequencystabilized(250kHzlinewidth)dyelaser(SirahMatisseDS).Pulseswerecreatedbyanacousto-opticmodulator(AAOptoElectronicMT200andMT110)indouble-pass,withanadditionalsinglepassAOMforsimultaneous2-colorexperiments,drivenbyanarbitrarywaveformgenerator(AgilentN8242A).Thelaserpowerwasabout100mWinfrontofthecryostatandthebeamfocusedbya75mmlensonthesample.Photonechoesweredetectedbya50MHzbandwidthavalanchephoto-diode(ThorlabsAPD110A)whichoutputwasprocessedandrecordedonadigitaloscilloscope(LeCroyWaveSurfer24Xs).Ashort-passlterwasusedinfrontoftheAPDtoreject uorescenceatwavelengthslongerthan600nm.Electricpulseswereproducedbya20MHzfunctiongenerator(HP33220A).Starkmeasurementsonthenanoparticlesusedaphotonechosequencewith=2andpulses1and1.5slongrespectively,witha3sdelaybetweenpulses.The3slongheterodynepulsewasshiftedby30MHz.Electricpulseswere1slongwithvoltagesupto1.25Vacrosselectrodesseparatedby0.5mm.Longersequenceswereusedformeasurementsonthe0.5%Eu3+YOtransparentceramic,thankstoits30scoherencelifetime.Thesample23was0.25mmthickandsynthesizedaccordingtotheproceduredetailedinRef.3SEMMsinglefrequencystorageusedinput,rstandsecondpulsesandheterodynepulsesof1,1.5,1and1sduration.Thedelaybetweeninputandrstpulseswasvariedbetween6and17s,whilethedelaybetweenecho1andthesecondpulsewasxedat3s.Electricpulseswere500nslongwithavoltageof1Vandwerealsousedforfrequency-multiplexedexperiments.StarkmodulatedechoindisorderedmediaWeconsideranelectriceldEorientedalongthezaxis.Theelectricdipolemomentdier-ence()andlightelectriceldpolarization(EL)directionsaredenedbythesphericalan-gles(;)and(L;L)respectively.AssumingauniformdistributionofandELdirections2

2andinthelimitofweakexcitation,theechoamplitudeinanensembleofcentro-symmetriccrystalsisgivenby:Z3jAj=A0D(;;L;L)cos(2kETScos)sinsinLddLddL(S1)whereDittheangularpartoftheprojectionofELonthetransitiondipolemoment,whichisparallelto.Itreads:D=jsincossinLcosL+sinsinsinLsinL+coscosLj:(S2)InEq.S1,integrationover;l(;L)iscarriedon[0;=2]([0;])interval.Intheexperimentsonthetransparentceramic,lightpropagatesparalleltoE,inthezdirection.Wechooseitspolarizationalongx,i.e.L==2andL=0.Eq.S1becomes:Z=24jAj=A0cos(2kETScos)(sin)d;(S3)0whereintegrationoverhasbeenincludedinA0.WithAS=ETS,thisexpressionisequivalenttoEq.3ofthemaintext.Fitstoexperimentaldata(Fig.1d,maintext)werecarriedoutbynumericalintegration.WenotethationswhichexperiencesmallStarkshifts,withnearlyperpendiculartoE,arealsocontributingthemosttotheechosignal.ThisresultsinalowereectiveStarkcoecientandshiftsthepointofzeroechoamplitudetoalargerStarkpulseareacomparedtonanoparticles(Fig.1d,maintext).Indeed,inthecaseofthenanoparticlepowder,wecanassumethatlightpropagateswithrandomdirectionandpolarization.Ionsthuscontributetotheechosignalindependentlyoforientation.WecanthereforekeepthetermsthatonlydependoninEq.S1integral.Thisgives:jAj=A0sinc(2kETS)=A0sinc(2kAS);(S4)wheresinc(x)=sin(x)=(x)andAS=ETSistheStarkpulsearea.Fig.S1shows3

3experimentaldataandtsbyEq.S4and4(maintext).Theformerreproduceswelltheamplitudeoscillationperiod,butnotitsdamping.ThiscanbetakenintoaccountbyanexponentialtermandisattributedtoelectriceldEinhomogeneity.FigureS1:EchoamplitudeinEu3+YOnanoparticlesasafunctionofStarkpulsearea.23DottedandsolidlinesaretstoEqs.S4and4(maintext)respectively.EchoandSEMMmemoryeciencyTwo-pulseechoandmemoryecienciesweredeterminedbymeasuringtheratiobetweentheintermediateecho1andtheoutputpulseintensitiesandtheinputpulseintensities.Valueswerethencorrectedfordephasingbyafactorexp(2=T2)whereistheevolutiontimebetweentheinputandecho1(output)pulses.Echo1hadaneciencyof1:2104,whereastheoutputpulseonewas6:5104.Thelatterhighereciencysuggeststhattherstrephasingreducestheeectof uctuations,eectivelyextendingcoherencelifetime.4Thesampleabsorbed17%oftheinputpulseand2-pulseechotheoreticaleciencyshouldbe14%inthesmallinputregimeandwithaperfectpulse.5Thelowerobservedecienciesareattributedtothestronglightscatteringinthepowderthatcausesinaccuraterephasing,becausethepulseareaisnotwelldened.Additionaleectsofscatteringbythepowderofthelaserpulses,theechoandtheheterodynedetectionarealsolikelytodecreaseeciency,althoughevaluatingsucheectsremainsdicult.6,74

4Thelowdelitypulsesarealsogeneratingalarge uorescenceatthetimewheretheoutputechoisemitted.Itsintensitywasabout3105largerthantheoutputpulseone.5

5MemoryphaseandamplitudedelityFigureS2:Outputpulserelativephasesfordierentinputrelativephases(th).Eachpointcorrespondstoasingle-shotacquisitionandiscalculatedfromtheFFToftheheterodynedetectionpulse.Themeanoutputphaseisrepresentedbyaradialline.Thelargescatteringofvaluesisduetolowsignaltonoiseratiosinsingle-shotmeasurements.6

6FigureS3:NormalizedrelativeoutputpulseamplitudesAR;output=(A1A2)=(A1+A2),whereA1(A2)istheamplitudeat-3(0)MHz,fordierentinputphases(seeFig.5,maintext).AmplitudesforthetwocolorsintheinputandpulsesweresetascloseaspossiblewithAR;input==0:060:06.AR;outputstandarddeviationacrossinputphasesis0.056,showingahighamplitudedelityforthestorageprocess.ThelinerepresentsAR;outputmeanvalue,0.097,whichisconsistentwithAR;input=.7

7ParticlescoupledtoacavityCavitiescanimprovequantummemoryeciencybyallowingnearlycompleteabsorptionandretrievaloflightformaterialswithlowopticaldepth.WefollowtheapproachofAfzeliusetal.8whereacavitywithlossesequaltothematerialabsorption(impedancematchedregime),andaprotocolbasedondoublerephasingasinSEMMareproposed.Theeciencyoftheoverallstorage/retrievalprocessisgivenby=16C2=(1+C)4,whereCisthecooperativityfactor.UniteciencyisobtainedforC=1.ForanensembleofNionsspanninganinhomogeneouswidth,thecooperativityisgivenbyC=4g2N=,whereisthecavitylinewidthandgtheatom-eldcoupling.Abercavitywithalengthof2m,amodewaistw=0:9mandanesseof1500009,100wouldresulting22MHzand=2500MHz.A100nm7%:Eu3+YOnanoparticle23wouldgiveaspectraldensityofN==27ions/MHz(assuminga27GHztotalinhomoge-neouslinewidth)andachieveC=0:64and=0:91overthecavitylinewidth,assumingperfectpulses.Sincedephasingisnottakenintoaccount,thiseciencycorrespondstostoragetimesmuchshorterthanT2.Placingseveralparticleswithlowerdopinglevelinthecavitycouldalsobepossible,providedthatscatteringdoesnotdecreasethenesse.Thiscouldbemitigatedbyplacingtheparticlesinanindexmatchedlayer.10Whileacavitywouldgreatlyimprovememoryeciencyandpulsedelitytoensureoutputemissioninanon-invertedmedium,itcanalsoleadtoaddednoise.8Asmentionedinthemaintext,SEMMisdesignedtosuppresscollectivenoisebypreventingrephasingofspontaneousphotonsemittedatthetimewhereecho1wouldbeemitted.The580nmtransitioninEu3+:YOparticleshasaverysmallemissionrateofabout12ph/s.The23cavitywillenhanceitbythePurcellfactorandwiththeaboveparameters,thenumberofspontaneousphotonsemittedina1=timeslotwillbeabout4.Asshowninthemaintext,SEMMwillreducethecorrespondingechobyafactoratleast104,resultinginanoiselevelcompatiblewithsinglephotonstorage.OthersourcesofnoisecanbeloweredbyworkingatstoragetimesTT.8ThecavityproposedabovewouldreduceTtoabout7s,S118

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