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Chapter 8 Quantum light（第1页）

Chapter8Quantumlight

InChapter1，Iiheideathatlightcouldbestruedasastreamofparticles，hotons’forsoutthatthesearerealparticles，roduced，playedwith，measured，stored，andusedfthings。However，eventhoughphotonsareihesimplestexpressionoflight，makingindividualphotonsisnotsosimple。Mostlightseofadifferentkind，forwhiumberofphotonsisnotfixed。

Alightbulb，forinstance，producesastreamofphotonsthatsprayseverywhere。Ifyoulookedatthelightgoingiionfromthebulb，andtheashorttemporalseofthebeam—atimeslot，ifyoulike—theoephotonsinthatslot。Butifyourepeatedtheexperimeimes，you’dfindthattheonswasraimeslargeaimessmall。Theaverageonswouldbefixed，dependihebulb，butyou’dosaywithtyhohotonsyouwouldmeasureiagive’soeristicsof‘classicallight’—lightthatbedestirelyintermsof>

&isalsoofthiskind。Theaverageonsinapulsehtbelarge，butfiveualonswillbebiggerorsmallerthahespreadofphotonnumbersinapulseisapproximatelythesquarerootoftheaveragehattherelative‘ionintheonsineachpulseparedtothemeannumberoverallpulses—getssmallerthehighertheaverageons。

Thusalaserbeamhasintriyhissetsalimitoyofimagesyougetwithlaserillumiionsiedetegtheseparationoftwopointsinanimageisimprefactitisveryimpreciseforlow-iylight，wherethemeanphotonnumberissmall（sotheobjectishardtosee）aioninphotonnumberfromframetoframeislarge。Theonlywaytogetprecisemeasurementsister，thusiheonsillumi，aheresultsovermanylaserpulses。Therelativeiynoiseisreducedbythissignalaveragioabetter-resolvedimage。Thepreproportiontothesquarerootoftheohisiscalledthe‘standardquantumlimit’，sinoclassicallightbeambeatit。

Quantumlight，oherhand，allowsyoutoachievemuchbetterresultsinsignalaveragingforthesameaverageoumlighthavemuoisethananyclassicallight。Butfirst，youhavetobuildaquantumlightsource。Therearemanykindsofsuchasource，eachprodugadistinlight。Butwemightsider，tobecrete，aseheprimitivequa—aphoton。

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Sohowakejustasingle，individualphoton?There’saverypracticalsveoFris1965。Hisideale。Takeasiomandputitiate（see

Chapter5foradisofhowtodothis）。Thenwaitforittodroptoitsgroudoes，itemitsjustoon，sine‘quantum’ybestorediom。Youtellwheomhasemittedthephotorethe‘kick’providedbythephotoum。Ifyoudeteoving，youdetermihatthesionisonitswayaioninwhichitisgoing。

Somemodernquantumlightsourcesoperateinasimilarwaytothis，onlytheycorraltheatombetweentwomirrors（anoptical‘cavity’similartothatofalaser），averyquicklysothatitemitspreferentiallyiiohecavityaxis。Thismakesareliablesourglephotons。Itisanespecially‘lownoise’sourcethephotoedwithstrictregularity。Ifyoulookedatagiveinsuchabeam，you’dbeabletopredictwithtyhohotonswouldbeinit—justoheiyisexallystable—itisa‘quiet’lightbeam，intrasttothe‘noisy’classie。

Theideaisalsousediumlightsourparticular，youstructaverysimplelightsicaleffects。Specifically，therearecrystalsthatephotonwithhigheobesplitintotwophotonswithly，eachabouthalfinalinputphoton。Theprobabilitythatthisfissiontakesplaceisrathersmall，formostmaterials。Butsionsareprodupairs，youeasa‘herald’，tosignalthepreseher（Figure34）。Suchlightsourcesaretheworkhorseofthefieldofquantumoptics，whichusesthequantummeicalfeaturesoflighttoexplorethefoundationsofquantumphysics，aswellastoenablenewkindsofinformationteologies。

Justasclassicaleleagicolarized，sos。Sowemightfiicallypolarized（V）photonorahorizontallypolarized（H）photon。Thesewouldbehavejustlikewaves，inthatifwemeasuredthepolarizatioopassedthroughapolarizerorientedhorizontally，thehattheH-photonalassedthroughaonnever。

34。A‘heralded’sionlightseingphotonsrandomly，butwithasignalthatindionehasbeenprepared。

What’sstrawestructadiagonallypolarizedphoton，osgwiththefieldat45degreestoboththehorizontalaical。Butifwenowtrytoseeifthephotohroughthehorizontalpolarizer，thenthereisanambiguity。Thephoto‘piece’oflight，so’tbedividedfurther。Howshoulditbehaveatthepolarizer?ensisthatitistrahaprobabilityofone-half，ahequalprobability（illustratedinFigure35）。

Ihatimpliesisthatifyoutrytheexperimentofputtingadiagonallypolarized（D）sionintoahorizontallyorientedpolarizeramilliohen500，000timesitwillgh。Arahingaboutquantummeicsisthatyouottellorialwhaten。ThisishephotonsideredsometimestobeH-polarizedaimesV-polarized。RatheritisbecausethephotonisbothHandV-polarized，simultaherandomouteasuremeon’spolarizationthereforerevealtheintrihatinhabitsthemostfualleveloftheuniverseasdescribedbyquantumphysics。

35。Adiagonallypolarizedphotoersapolarizer，asrandhoortheother。

Ofakeavirtueoutofyinsuchces。Youdopractigswithsionsthatareunimagihht。Forihispropertyofphotoogeerandomnumbers，bymeasurihephotonistransmitted（labellie，say，1）orreflected（labelled0）。Therahestringofzeroesandonesisiheunderlyingphysiotjustiureandgofdice，ehisreasonquantumraorsareanemergingbusiness—you’tfaketheraheyprovide。

Aseple:youmakeunislinksforwhichthesecurityisguarahelawsofphysics，ratherthanbytrustingyourtelessupplier。Thisisbeportaiesofphotons。First，youotdetetwoplace。Forthatreason，ifaneavesdrrabsthephotontocapturetheinformati，thenofcourseyoudohephoton。Soyoureation，ahatsomething’swrong。

Butiftheeavesdropperisclever，shewillseonthatshehopeswillfakethemessage。Butyoutellthatit’safake!Thereasonyouowthisisthatinquahereistellyaboutasiumparticle。

siderthefollowingsario。Youwanttosendasimplebinarymessage（0sahislink，sayaverticallypolarizedphotonfor0andadiagonallypolarizedphotonfor1。Iftheeavesdropper（usuallyknownasEve）measuresthephotoheaicallypolarized’，sheotbethatthephotonwasa0，sihediagonallypolarizedphotonwouldgiveherthesamealeasthalfthetime。Soshegetssomeinformation，buthing。

hesehemessage（allycalledAlice—you，thereceiver，areBob）sendsyouaphotoncodedas1。Let’ssayEvemeasuresthisiitatiosapositiveresult。Shemustchoosewhethertosendyouaverticallyonallypolarizedphotoegyistosendyouaverticallypolarizedphotohemostlikelysourceofherresult。hediagonalpolarization。IfyourphotonisfromEve，itwillgiveyresult50pere。IfitisfromAlice，youwillhewro。SobypariionofthereceivedmessagewithwhatAlit，youtellifEveistamperingwithyourline。

Hhtbeevencleverer。ShemaytrytocopythephotonfromAlieasuringit。Sheaketwofagyinal。Thenshemakeaverticalpolarizatioononedadiagonalpolarizatiohesedshewouldhavedetermihefullinformationaboutthephoton‘bit’thatAlityouwithouty。However，shewouldbethwarted。Aremarkablefeatureofquantummeicsisthatthereisnopossibilityofbuildingaaethatakeareplica，ore，ofasiiunknownquaissimplyforbiddenbythelawsofphysics。Becauseofthesetosedbyphysient’and‘nog’—itispossibletobuildaseunislinkthatsmitasecretstreamofrandombitsbetweenAlidyou。

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