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ThisarticleispublishedwithopenaccessatSpringerlink.
comcsb.
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comwww.
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com/scp*Correspondingauthor(email:wpzhang@phy.
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cn)ReviewSPECIALTOPICJune2012Vol.
57No.
16:19251930QuantumInformationdoi:10.
1007/s11434-012-5101-7SqueezingbandwidthcontrollabletwinbeamlightandphasesensitivenonlinearinterferometerbasedonatomicensemblesJINGJieTai1,2,LIUCunJin1,2,ZHOUZhiFan1,2,HUDELISTFlorian1,2,YUANChunHua1,CHENLiQing1,2,LIXiaoYun1,QIANJing1,ZHANGKeYe1,ZHOULu1,MAHongMei1,DONGGuangJiong1,2,OUZeYu1,2,3&ZHANGWeiPing1,2*1QuantumInstituteforLightandAtoms,DepartmentofPhysics,EastChinaNormalUniversity,Shanghai200062,China;2StateKeyLaboratoryofPrecisionSpectroscopy,EastChinaNormalUniversity,Shanghai200062,China;3DepartmentofPhysics,IndianaUniversity-PurdueUniversityIndianapolis,Indianapolis,Indiana46202,USAReceivedDecember12,2011;acceptedFebruary13,2012Wereviewourrecentexperimentalprogressinquantumtechnologyemployingamplificationeffectoffour-wavemixinginarubidiumvapor.
Wehaveproducedanintensitydifferencesqueezedlightsourceatfrequenciesaslowas1.
5kHzwhichissofarthelowestfrequencyatwhichsqueezinghasbeenobservedinanatomicsystem.
Moreover,wefindthatthebandwidthofoursqueezedlightsourcecanbecontrolledwithlightintensitypumping.
Usingournon-classicallightsource,wehavefurtherdevel-opedanonlinearMach-Zehnder(MZ)interferometer,forwhichthemaximumfringeintensitydependsquadraticallyontheinten-sityofthephase-sensingfieldatthehigh-gainregime,leadingtomuchbettersensitivitythanalinearMZinterferometerinwhichthebeamsplittershavethesamephase-sensingintensity.
Thequantumtechnologiesdevelopedbyourgroupcouldhavegreatpotentialinareassuchasprecisionmeasurementandquantuminformation.
atomicensemble,fourwavemixing,quantumlightsource,nonlinearinterferometerCitation:JingJT,LiuCJ,ZhouZF,etal.
Squeezingbandwidthcontrollabletwinbeamlightandphasesensitivenonlinearinterferometerbasedonatomicen-sembles.
ChinSciBull,2012,57:19251930,doi:10.
1007/s11434-012-5101-7Photonsarenaturalfastcarriersofquantuminformation.
Forthisreason,muchattention[1,2],particularlyoverthelasttwodecades,hasbeendrawntowardsapplicationsofquantumopticalsystemstoquantuminformationprocessing,suchasquantumcommunicationanddistributedquantumnetworks.
Theresearchnecessitateshigh-qualityquantumlightsourcesthatgeneratesqueezedlightwithlargenoisesuppressionbelowtheshotnoiselevel(SNL)andentangledstates.
In1985,Slusheretal.
pioneeredsqueezedlightgenera-tionbasedonfour-wavemixing(FWM)inanopticalcavity[3].
Sincethen,severalmethodshavebeenexploredtoob-tainsqueezedstates;afundamentalandfrequently-usedtechniqueistheopticalparametricoscillatorconsistingofnonlinearcrystalsandcavitiestobuildupnon-classicalstatesveryefficiently[4–7].
Usingsuchmethods,verystrongsinglemodesqueezinghasbeenrealizedinthepastfewyears.
Forexample,vacuumsqueezinglevelsof10dBwereachievedin2008[8]andMehmetetal.
obtainedupto11.
5dBsqueezinglastyear[9].
Bycontrast,withoutanyopticalcavityandmodecleaner,FWMhasgraduallybe-comeanotherpopularmethodbecauseofitssimpleexperi-mentalsetup.
SincetheinitialworkofLett'sgroupin2007[10],asmuchas9.
2dBsqueezinghasbeenreportedinhotrubidiumvapor[11].
BasedonFWM,apairofmulti-spatial-modebeamswasproduced,carryingtwoimageswhichareinnon-separablecontinuous-variableentangledstates.
Theimageswerecomposedof"squeezedvacuum"twinbeams1926JingJT,etal.
ChinSciBullJune(2012)Vol.
57No.
16thatarestronglyentangledwhenprojectedontoarangeofdifferentspatiallocaloscillatormodes[12].
Squeezingbandwidthandlowfrequencysqueezingareimportantcharacteristicsofsqueezedphotonicstatesfortheirpotentialapplications.
Squeezedlightwithlowfre-quencywasfirstproposedtobeusedinhigh-sensitivitydetection[13].
Uptonow,manygroupshavesuccessfullygeneratedlowfrequencysqueezingatthesub-megahertzrange[1417].
Recently,low-frequencysqueezingwasfoundtobeinterestingforelectromagnetically-inducedtranspar-ency-basedquantuminformationprotocolsandotherappli-cationsatatomictransitionwavelengths[16].
Ourwork[17]isderivedfromthismotivationandinspiredbypreviousworksuchasthecreationofbeamswithalow-frequencyquantumcorrelationbasedonFWMinahotrubidiumvapor[18].
Wehavegeneratedanintensitydifferencesqueezedlightsourceatfrequenciesaslowas1.
5kHzwhichissofarthelowestfrequencyatwhichsqueezinghasbeenobservedinanatomicsystem.
Furthermore,wedemonstratethatwecanusepumpinglightintensitytocontrolthebandwidthofoursqueezedlightsource.
Thequantumlightsourcegeneratedinourexperimentcouldhavegreatpotentialintheapplicationofpreciseme-trologyandquantuminformation.
Therefore,wehaveex-tendedourquantumlightsourcetorealizeanonlinearMZinterferometer[19],whichwasproposedbyYurkeetal.
in1986[20].
Incontrastwithpreviousopticalinterferometersusinglinearopticalprocessing,ourexperimentshowsthatthemaximumfringeintensityofthenonlinearMZinter-ferometerhasaquadraticrelationtotheintensityofthephasesensingfieldinthehighgainregime,andthushasgreatpotentialtoreachtheultimatequantumlimitofphasemeasurement,i.
e.
theHeisenberglimit[21].
Inthefollowing,wepresentareviewonourexperi-mentalprogressofahighqualityquantumlightsource[17]andanonlinearMZinterferometer[19].
Thispaperisorga-nizedasfollows.
Section1introducesourrecentprogressinquantumlightsourceusingtheFWMprocessinrubidiumvaporatomicensemble.
ThenonlinearinterferometerusingtheFWMprocessasbeamsplittersisreviewedinSection2.
ConclusionsaresummarizedinSection3.
1QuantumlightsourceInthissection,wereporttherealizationoflow-frequencyandcontrollable-bandwidthsqueezingbasedonanondegen-erateFWMprocessinahotrubidiumvaporattheopticalD1transition.
WeperformedourexperimentusingaTi:sapphirelaser(Spectra-Physics)tunedabout1GHztotheblueoftheD1lineofrubidium(5S1/2→5P1/2,795nm)withalinewidthofabout30kHz.
Thislasersuppliescoherentlightusedtointeractwithrubidiumatomsinahotvaporcell,resultinginastrongFWM,ornonlinearphaseinsensitiveamplificationprocessandgeneratescorrelatedtwinbeams,theprobeandtheconjugate,witha6GHzfrequencydifference.
Figure1showstheenergydiagramofthe85RbD1linewhichformsadouble-systemandtheschematicdiagramoftheexperimentalsetup.
Theoutputpowerofthelaseris1W.
Apolarizingbeamsplitter(PBS)isusedtosplitthebeamintoaweakseedprobebeamandamuchstrongerpumpbeam.
Theseedbeamisred,detunedabout3GHzusinganacousto-opticmodulator(AOM)(Brimrose).
TheAOMisdrivenbyanRFsignalgenerator(Agilent,N9310A).
Thepolarizationsofthepumpandprobearechosenperpen-diculartoeachother,sothepumpfieldcanbefilteredoutafterthevaporcellwithaGlan-Thompsonpolarizer,whichisusedtocombinetheweakprobeandstrongpumpwithanangleof0.
4°.
Thecrossingpointisinthecenterofa12mmlongvaporcellwhichisfilledwithisotopically-pure85Rbandheatedto120°C.
Bothfacesofthecellareantireflectioncoatedtoachieveatransmissionefficiencylargerthan98%.
Thepumpbeamwaistatthecrossingpointis550m,whereastheprobebeamwaistis300m.
Theamplifiedprobeafterthevaporcellalongwiththegeneratedconju-gatewiththesamepolarizationareseparatedfromthepumpbeambyanotherGlan-Thompsonpolarizerwithanextinc-tionratioof105:1.
Theprobeandconjugatearedirectlysenttoabalancedphotodetector(BPD,ThorlabsPDB150)withtwohigh-quantum-efficiency(96%)photodiodes.
TheBPDsubtractsthephotocurrentswithaswitchablegain(usually105V/A)andsendsthesignaltoaspectrumana-lyzertoperformanoiselevelanalysisoveracertainfre-quencyrange.
Witha400mWpumpanda10Wprobeseed,theFigure1(Coloronline)Top:experimentalsetup.
PBS,polarizingbeamsplitter;AOM,acousticopticalmodulator;GL,Glan-laserpolarizer;GT,Glan-Thompsonpolarizer;M,mirror;BPD,balancedphotodetector;SA,spectrumanalyzer.
Bottom:energyleveldiagramofthe85RbD1line.
P,pump;Pr,probe;Conj,conjugate;,onephotondetuning;,twophotondetuning;vHF,hyperfinestructure.
JingJT,etal.
ChinSciBullJune(2012)Vol.
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161927amplifiedprobeisabout80Wandtheconjugateisabout70W.
Thetransmission(90%)oftheprobeismeasuredbyblockingthepump.
BoththeprobeandconjugatearesenttotheBPD,theintensitydifferencenoisebetweentheprobeandtheconjugateissubtractedandthenanalyzedbyaspectrumanalyzer(AgilentE4411B),asseeninFigure2.
TomeasuretheSNL,weguideacoherentlaserbeamofpower150W,equivalenttothetotalpoweroftheprobeandconjugate,splittingit50/50andsendingtheresultingbeamstotheBPD.
Themeasurementistakenwith100kHzresolutionbandwidth(RBW)and1kHzvideobandwidth(VBW).
Weinvestigatedthesqueezingpropertiesinthelow-frequencyregionwiththepumppowersetto400mW.
WeuseafastFouriertransform(FFT)spectrumanalyzer(SRSSR770)withbandwidthspanningfromtheDCto100kHz.
AsseeninFigure3,weobservetherelativeintensitysqueez-ingofan80Wprobeanda70Wconjugateatfrequen-ciesaslowas1.
5kHz.
Thisis,tothebestofourknowledge,1kHzlowerthanthepreviousbestresultobtainedfromanatomicsystematthiswavelength.
TheRBWoftheFFTspectrumanalyzeris31.
25Hzforthismeasurement.
Anotherimportantcharacteristicisthesqueezingband-width.
Alargebandwidthisalwaysusefulforcommunica-tions;inparticular,squeezedlighthasbeenproventobeaFigure2(Coloronline)Noisepower.
(a)SNL,(b)intensitydifferencesqueezingbetweentheprobeandtheconjugate,and(c)thebackgroundnoiselevel.
100kHzRBWand1kHzVBW.
Figure3(Coloronline)Low-frequencynoisepowerspectrumfromtheFFTspectrumanalyzerwith31.
25HzRBW.
(a)SNLand(b)intensitydifferencesqueezingbetweentheprobeandtheconjugate.
goodsourceforquantumcommunication.
Mostlikely,squeezedstateswithlargebandwidthwillbegoodcandi-datesforfuturehighefficientquantumcommunication.
Inourexperimentsystem,wefoundthepumppowerhasacapacitytocontrolthesqueezingbandwidthofthisFWMamplifier.
Wechangethepumppowerfrom100to700mWwiththeotherparametersfixedandmeasurethesqueezingbandwidthasshowninFigure4Wecanseeastronglinearrelationshipbetweenthesqueezingbandwidthandthepumppower.
2NonlinearMach-ZehnderinterferometerAsimpleinterferometersuchastheMach-Zehnderinter-ferometershowninFigure5(a)consistsoftwobeamsplit-terswithoneactingasawavesplitterandtheotheraswavecombiner.
Forsimplicityofargument,wetaketheseasbe-ingidenticalwiththesametransmissivityTandreflectivityR.
Fromanystandardopticstextbook,theoutputintensityisrelatedtotheinputbyout0F21cos21cos2,IITRI(1)whereI0istheinputintensityandIF=4I0TRisthemaximumfringeintensity.
Thebestsensitivityformeasuringasmallphasechangeoccursat=/2withoutFps2,2IITI(2)whereIps=RI0istheintensityofthefieldsubjecttoaphasechange(phase-sensingfield).
Thus,thesensitivityforphasemeasurementisdirectlyrelatedtothefringeintensityIFandforalinearinterferometerisalsoproportionaltothephasesensingintensity.
Moreover,therearesomenonlinearprocessesthatarephasesensitive.
Yurkeetal.
proposedin1986[20]tousepar-ametricprocessestomeasurephasesandultimatequantumFigure4(Coloronline)Left:squeezingwithpumppowerat100mW(top)and700mW(bottom).
(a)showsSNLand(b)issqueezing.
Right:squeezingbandwidthversuspumppowerwithmeasureddata(dots)inourexperimentandlinearfitofthedata(straightline).
100kHzRBWand1kHzVBW.
1928JingJT,etal.
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16limits,i.
e.
theHeisenberglimit,canbeachievedinsensitiv-itiesofphasemeasurements[21].
Therewerenumeroustheoreticalanalysesonsuchasystem,includingtherecentPlicketal.
analysissuggestingafurtherboostfromaco-herentstateinjection[22].
However,sinceitsinception,therehasbeennoexperimentalrealizationperhapsbecausetheoutputfieldintheoriginalproposalbyYurkeetal.
isveryweaktodetectatexperimentally-controllablegain.
Inthispart,wereportonanexperimentinwhichweconstructanonlinearinterferometerwithparametricamplifiersactingasbeamsplitterstosplitandrecombineanincomingopticalfield.
Ifproperlybalanced,theinterferometercaninprinci-plehave100%visibility.
Sinceamplificationisactivelyinvolvedintheinterferometer,thephasesensingfieldinsidetheinterferometerisamplifiedfromtheinputfieldandsoistheoutputfieldexhibitingtheinterferencefringe.
Thus,thesensitivitycanbegreatlyenhancedascomparedtothetra-ditionallinearinterferometer.
ConsidertheschematicsketchinFigure5(b).
Ourinter-ferometerconsistsoftwoparametricamplifiers,PA1andPA2.
Thefirstamplifiestheinput"signal"fieldandgener-atesaconjugate"idler"field;thus,PA1servesasabeamsplitter.
Thesecondservesasabeamcombinerthatmixesamplifiedsignalandfields.
Theactionofaparametricam-plifieriswelldescribedinanynonlinearopticstextbook[23]asoutinin*outininssiiis;,AGAgAAGAgA(3)wheresandistandforsignalandidler,respectively;Gistheamplitudegainoftheamplifier;and221Gg.
Therefore,ifthereisnoidlerfieldinputatPA1,thefieldsafterPA1is*s11s0i11s0;.
AGAAgA(4)Here,As0istheinputsignalfield.
Notethatwhenthegainislarge,G1≈g1>>1,andwehaveanearly-equalsplittingofAs0butthesplitfieldsareamplifiedfromtheinput.
Assum-ingtheidlerfieldissubjecttoaphaseshiftof,weobtainfromeqs.
(3)and(4)thePA2outputs*s2s0i2s0AGAAgA(5)with**12121221()e;()e.
iiGGGgggGgGg(6)Ifbothamplifiershavethesamegain:G1=G2=G0;g1=g2=g0,wehave(G0,g0=real)2000()11e;()1e.
iiGggGg(7)Fromeq.
(4),wefindtheintensityofthephasesensingfield(idler1)insidetheinterferometeras22i1i100IAgI(8)with20s0IAastheinputintensity.
Theintensitiesoftheoutputfieldscanalsobeeasilyobtainedas22s2000i200012(1cos),2(1cos).
IIGgIIGg(9)Thusboththeoutputfieldsshowinterferencefringeswhenthephaseisscanned.
Theidlersidealwayshasavisibilityof100%,butthesignalside'svisibilityis22s0000212,VGgGg(10)whichiscloseto100%ifG0≈g0>>1.
Fromeq.
(9),wefindthemaximumfringeintensityattheidleroutputtobe22Mi20000psps0ps0444.
IIGgGIIIII(11)Herepsi1IIistheintensityofthephasesensingfield.
ForalargegainandafixedinputI0,wehaveIps>>I0andM2i2psII.
Eq.
(11)isthemainfeatureofthisnonlinearinter-ferometerthatisdifferentfromatraditionallinearinterfer-ometer,i.
e.
,themaximumfringeintensitydependsquadrati-callyonthephase-sensingintensity,incontrasttothelineardependenceineq.
(1)foralinearinterferometer.
Further-more,themaximumfringeintensityisamplifiedfromthephasesensingintensitybyafactorof4|G0|2,givinganen-hancementinsensitivityascomparedtoeq.
(2)foralinearinterferometer.
Figure5(a)AlinearMach-Zehnderinterferometer.
(b)Anonlinearinterferometerwithparametricamplifiers(PA1andPA2)astheequivalentbeamsplitters.
JingJT,etal.
ChinSciBullJune(2012)Vol.
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161929TheexperimentallayoutisshowninFigure6.
WeusetwoidenticalRbvaporcellsastwoparametricamplifiersbasedontheFWMprocess.
Initiallywehavealltheexper-imentalparametersmentionedinSection1toobtainahigh-intensitydifferencesqueezingofsignalandidler,whichmeansproducinghighly-correlatedtwinbeams.
Next,usinga4fimagingsystem,wecoupletheoutputsofthefirstvaporcell(theamplifiedsignalandtheconjugateidlerbeams)intothesecondvaporcellthroughanotherGlan-laserpolarizer.
Thesearesymmetricallycrossedwiththepumpatthecenterofthesecondvaporcellat0.
7°,similartothefirstvaporcell.
Thetwooutputbeamsfromthese-condvaporcellaresenttotwophotodiodes(D1andD2)withsingle-modefibercouplingforspatialmodecleanup.
Theresultingphotocurrentsarefedtoadigitalscopefordatacollectionandanalysis.
Amirrormountedonapiezo-electrictransducerisusedtochangethephaseofthesignalandidlerbeamsafterthefirstcellforthephasescanoftheinterferometer.
TherelativepowerofthepumpbeamscanbecontrolledbyhalfwaveplatesH1,H2,andH3whilethepoweroftheinjectedsignalbeambyH4.
Figure7showstypicalinterferencefringesatthetwooutputsoftheinterferometer.
Thesignaloutputhasaslightlysmallervisibility(94.
5%)thantheidlerside(98.
6%),asexpectedfromeq.
(10).
Next,wemeasurethevisibilitiesatdifferentgainsoftheparametricamplifierbyvaryingthepowerofthepumpbeams.
Figure8showstheresultsofthemeasurement.
Theredsolidlineisaplotofeq.
(10)multi-pliedbyafactorof0.
95toaccountforimperfectalignmentoftheinterferometer.
Thevisibilitydataofthesignalfringefollowthislineverywell.
Moreover,thevisibilityoftheidlerfringeiskeptconstantataround95%,consistentwitheq.
(9).
Toconfirmthenonlinearnatureoftheinterferome-ter,wemeasurethemaximumoftheinterferencefringeoftheidleroutputasafunctionoftheintensityofthephasesensingfield(theidlerbeambyD3rightafterthefirstvaporcell)aswechangethepumppowers.
TheresultsareplottedinFigure9inlog-logscale.
Thesolidredlineisabestfitcurvetoeq.
(11)withI0astheadjustableparameter.
Thedashedblacklineisastraightlinewithaslopeoftwo,showingthequadraticdependence.
Theinsetisinlinearscaleclearlyshowingthenonlineartrend.
Notethat,atthehighestvalue,themaximumfringeintensityisabout30timesthephasesensingintensity.
3ConclusionsWithparametricamplificationbasedonFWMinrubidiumvapor,wehaveforthefirsttimedemonstratedgenerationofFigure6(Coloronline)Experimentallayoutofthenonlinearinterferometer.
H,halfwaveplate;PBS,polarizationbeamsplitter;AOM,acousticopticmodulator;GL,Glen-laserpolarizer;GT,Glen-Thompsonpolarizer;SMF,single-modefiber;D,detector.
Figure7(Coloronline)Interferencefringesforthenonlinearinterferometer.
(a)Signaloutput.
(b)idleroutput.
1930JingJT,etal.
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16Figure8(Coloronline)Visibilityofinterferencefringeasafunctionofpowergain|g0|2.
Greensquares,idlerfringe;bluediamond,signalfringe;redsolidline,plotofVsineq.
(10).
Toaccountforimperfectalignment,Vsismultipliedbyafactorof0.
95.
ThearrowcorrespondstothegainforFigure3.
Figure9(Coloronline)Dependenceofthemaximumintensityoftheinterferencefringeontheintensityofthephasesensingfieldinsidethenonlinearinterferometerinalog-logscaleplot.
Dashedline,slope2forquadraticdependence.
Inset,linearscaleplot;redsolidline,fittothefunc-tionineq.
(11).
strongcorrelatedtwinbeamswith5dBintensitydiffer-encesqueezing.
Withsqueezingfrequencieswasaslowas1.
5kHz,thesqueezingbandwidthwascompletelycontrol-lable.
Further,usingtwocascadeFWMprocesses,wecon-structedanonlinearMZinterferometerthathasmuchhigherphasesensitivitythanalinearMZinterferometer.
OurexperimentalachievementofahighqualityquantumlightsourceandanonlinearMZinterferometercouldbeofpotentialapplicationinultra-highprecisionmeasurementsandquantuminformationprocessing,aswellasultracoldatomexperiments.
ThisworkwassupportedbytheNationalBasicResearchProgramofChi-na(2011CB921604and2011CB921602),theNationalNaturalScienceFoundationofChina(10974057,11004057,11004058,11004059,11034002and10874045),ShanghaiPujiangProgram(09PJ1404400),theProgramforProfessorofSpecialAppointment(EasternScholar)atShanghaiInsti-tutionsofHigherLearning,theProgramforNewCenturyExcellentTal-entsinUniversity(NCET-10-0383),"ShuGuang"ProjectofShanghaiMunicipalEducationCommissionandShanghaiEducationDevelopmentFoundation(11SG26),theScientificResearchFoundationfortheReturnedOverseasChineseScholars(StateEducationMinistry),the"ChenGuang"ProjectofShanghaiMunicipalEducationCommissionandtheShanghaiEducationDevelopmentFoundation(10CG24).
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