S eminaire Poincar e      S eminaire Poincar Experiments with single photons Philippe Grangier  Back to the beginning  Einsteins  and  articles The birth of the light quanta  licht quanten in their o
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S eminaire Poincar e S eminaire Poincar Experiments with single photons Philippe Grangier Back to the beginning Einsteins and articles The birth of the light quanta licht quanten in their o

Interestingly several points epressed in a very collegial style in this article were eposed again in a ore direct einsteinian style in a conference 2 thatEinsteingaveinSalburgonsepteber211909ThisconferenceentitledTheevolutionof our conceptions about

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S eminaire Poincar e S eminaire Poincar Experiments with single photons Philippe Grangier Back to the beginning Einsteins and articles The birth of the light quanta licht quanten in their o

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S eminaire Poincar e 2 (2005) 1 – 26 S eminaire Poincar Experiments with single photons Philippe Grangier 1 Back to the beginning : Einstein’s 1905 and 1909 articles The birth of the light quanta - “licht quanten” in their original version - is rightfully associated with the article [1] published by Albert Einstein in 1905, “An heuristic point of view about the production and transfor%ation of light”. Interestingly, several points e(pressed in a very collegial style in this article were e(posed again in a %ore direct, “einsteinian” style, in a conference [2]

thatEinsteingaveinSal+burgonsepte%ber21,1909.Thisconference,entitled“Theevolutionof our conceptions about the nature and the constitution of radiation” reveals, and to so%e e(tend co%pletes,thewayofthin,ingthatleadEinsteintothe1905papersonrelativityandradiation. For instance, in 1909 Einstein gives again the list of open proble%s in the radiation theory, whichbrie.yalludedtointhe1905article.Theseproble%swere: 1. why does the appearance of a photoche%ical reaction depends only on the colour of light, andnotonitsintensity? 2. why is short wavelength radiation generally %ore active che%ically

than long wavelength radiation? 3. why is the ,inetic energy of cathode rays 2electrons3 produced by the photoelectric e4ect independantonthelightintensity? 5. how to e(plain the lac, of “energy dispersion” observed with 6 rays : secondary 6-rays, produced fro% electrons generated by pri%ary 6-rays, %ay recover al%ost all the initial energy,whilethisenergyshouldbe“spreadout”infreespace. This last point appears so surprising to Einstein that he writes : “Fro% this point of view, it see%s that Newton8s e%ission theory contains %ore truth than the wave theory, since it says that the energy given

to a light particle when it is e%itted is not spread out in in9nite space, but re%ains available for an ele%entary absorption process.” It is then clear that Einstein wants to show that all these e4ects beco%e understandable, if one ad%its that “the energy of light is distributedinadiscontinuouswayinspace,aslocali+edquantawhichcan%ovewithoutdivision, andwhichcanbeabsorbedore%ittedonlyasawhole”. Anotherpointclearlyapparentin1909isthatEinstein,thoughhefullyad%ittedthatPlanc,8s for%ulacanonlybetrue,wasreallyshoc,edbyanyatte%ptto%a,ePlanc,8shypothesisco%pat-

iblewiththeclassicaltheoryofradiation.Hewritesforinstance:“One%ightbelieve,byloo,ing atthis2Planc,8s3de%onstration,thatPlanc,8sfor%ulacanbeconsideredasaconsequenceofthe presenttheoryofradiation.However,thisisnotthecase,forthefollowingreason”.Thenhepoints outonasi%plee(a%plethattheenergyquantu% h %aybe%uchlarger26 =10 ti%eslargerin his e(a%ple3 than the %ean energy of one oscillator. It thus appears that the energy should only ta,e the values +ero, 6 =10 ti%es the %ean energy, or a %ultiple of this quantity. This is clearly in plain - and even shoc,ing - contradiction with Ma(well8s

electro%agnetic theory. Einstein8s conclusion is thus : “Would it be possible to consider that this for%ula is true, but to provide a de%onstrationthatdoesnotrelyonanhypothesiswhichisso%onstruousat9rstsight?”. In order to solve the dile%%a, Einstein uses again ther%odyna%ics, one of his favourite tools, and he concludes that in the do%ain of validity of Wien8s law 2the “quantu%” do%ain3, a %onochro%aticradiationbehavesasifitwasco%posedofindependantenergyquantawithasi+e h .Interestinglyagain,hegoesevenfurtherinthe1909conference2aswellasinanotherarticle[3]
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P. Grangier S eminaire

Poincar publishedalsoin19093,andidenti9estwobasiccontributionstothe.uctuationsofradiation:one isa“particle-li,e”contribution,thatwewouldcallnowshot-noise,andtheotheroneisa wave- li,e” contribution, which is due to rando% interferences, and that we would call now spec,le-li,e .uctuations,ortheHanbury-BrownandTwisse4ect.Itisalsoreallyre%arquablethathispaperof 1925aboutaperfectgasobeyingtheBose-Einsteinstatistics[5],herecoversthesa%etwoter%s, withthesa%einterpretation-e(ceptthatitappliesnowto“particles”andnotto“radiation”.In that case, the “particle-li,e” ter% appears natural, while the

occurrence of a “wave-li,e ter%” is used by Einstein as a basis to a introduce “a very re%ar,able publication” by Louis de Broglie, whichshows“howtoassociatea2scalar3wave9eldtoa%aterialparticle”B To our %odern eyes, it is thus clear that through his deep analysis of ther%odyna%ical .uctuations,Einsteinwasabletocapturetheessentialfeaturesofquantu%obCects,which,whatever theyare“classically”,cane(hibitboth“particle-li,e”and“wave-li,e”.uctuations.Attheendof his 1905 article, Einstein %oves 9nally to his initial %otivation, which was to solve the %ysteries

onthephotoche%icalandphotoelectrice4ectsbyusingthelighquantu%hypothesis.Hecanthus interpret Sto,es8 law, and he gives the fa%ous for%ula for the ,inetic energy of the electrons producedbythephotoelectrice4ect,whichwillbeveri9edin1916byMilli,an. Despitetheseveryconvincingargu%ents,thelightquantu%hypothesiswasthelesssuccessful a%ongthethree1905papers,inthesensethatitwasquasi-unani%ouslyreCectedbythescienti9c co%%unity.Apparently,thoughEinsteinhasinsistedvery%uchthatthecontradictionwithclas- sical electro%agnetis% was already present in Planc,8s hypothesis, the bla%e was put on hi% for %a,ing it

too “visible”. Also, %any physicists were advocating that the light %ight “trigger” the photoelectrice4ect,ratherthandirectlyinduceit.Nevertheless,the%indsslowlyevolved,andthe lastenne%iesofthelightquantu%vanishedafterthee(peri%entsdonebyEo%ptonatthebegin- ningofthe208s,ontheenergy-%o%entu%conservationinthecollisionbetweenanelectronanda 6-rayphoton.TheNobelpri+ewasattributedtoEinsteinin1921,“forhisservicestoTheoretical Physics, and especially for his discovery of the law of the photoelectric e4ect”. In 1926 Gilbert Lewisinventedthena%eof“photons”,bywhichthelightquantahavebeen,nowneversince.

Onecenturylater,whatcanwelearnfro%theseolddebates?We%ay9rstre%e%berPlanc,8s fa%ous quotation, “truth never triu%phs, but its enne%ies eventually die”. First, it is clear that Einstein8s argu%ents on the .uctuations were e(tre%ely strong, and should have been enough to convince his colleagues. On the other hand, the situation about the photoelectric e4ect itself was actuallynotsoclear.Actually,ithasbeenshownlaterthatphotoe%ission,ta,enbyitself,doesnot really “prove” the quanti+ation of the light. This can be reali+ed by calculating [5] the ioni+ation probability of quanti+ed ato%s sub%itted to

a classical 2wave-li,e3 9eld oscillating at frequency : one does 9nd the energy threshold e4ect, and even Einstein8s for%ula. But then h appears fro% Fer%i8s golden rule, due to Bohr8s for%ula G2 initial final /h , rather than fro% the 9eld quanti+ation. Though the consistency of such a “se%i-classical” %odel can be questioned, a full proof of the quanti+ation of the 9eld fro% photocounting events had yet to co%e. Of course, isolatingasinglephotonwouldhaveputthisa%biguitytoanend.Butinspiteofitsearlybirth,a single photon had never been “seen” for the 9rst eighty years of its e(istence,

essentially because ithadnotbeenpossibletocontrolhowindividualphotonsaree%ittedbyalightsource. 2 Quantum optics and the photon. Thingsstartedtochangebetweenthelate19608sandearly19H08s,withthee%ergenceofquantu% optics, a discipline dedicated to the study of the quantu% properties of light and, of course, of photons. It was then reali+ed that quantitative discrepancies between the fully quanti+ed and se%i-classical descriptions of light-%atter interaction can hardly be found by loo,ing at single photodetectionevents,butthattheyappearstraightforwardlywhenloo,ingatcorrelationsbetween

several-inpractice,atleasttwo-photodetectionevents. Since the proof of the photon is the “seeing”, the 9rst question that could be as,ed was “if we so%ehow can isolate a single photon, how can we see that we actually have one and only one photon?” A clever tric, is to send that un,nown state of light onto a bea%splitter 2i.e. a half- silvered%irror3,sothathalftheintensityisre.ectedandhalfistrans%itted.Sinceasinglephoton
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Vol. 2, 2005 Experiments ith single photons 3 Pump Laser Diamond sample Pinhole Filters Dichroic mirror NA 1.3 Confocal Microscope 50/50 Beam- splitter

Avalanche photodiodes Time -to- Amplitude converter 40 20 -20 Normalized light intensity autocorrelation Delay (ns) Photon counting Figure1:Modernversionofanantibunchinge(peri%ent:Asinglee%ittingdipole2hereacolour center in a dia%ond nanocrystal3 is irradiated by a continuous-wave green laser. The red .uo- rescence fro% the center is collected and split towards two photon-counting detectors 2avalanche photodiodes3.Thenu%berofcoincidencecountsvanishesat+erodelay2i.e.forsi%ultanenousde- tections3,andincreasesatlaterti%es:this“antibunchinge4ect”isthesignatureofthequantu%

characterofthelighte%ittedbyasingledipole. cannotbesplitintotwohalves,itwill either bere.ected or trans%ittedwith50I50probabilities, butwillnevergobothwaysatonce.So,ifsensitivephotodetectorsaresetineachofthetwooutputs of the bea%splitter, the probability of both detectors producing an electric pulse si%ultaneously willbeata%ini%u%,inotherwordsthetwopulseswillneverbebunched.A9rste(peri%ent[6] alongtheselineswasreali+edbyJohnElauserin19=5,andthenthe“antibunching”e4ect[=]itself was observed in 19=6 by Leonard Mandel and cowor,ers in Rochester 29g. 13. It clearly appeared

asapheno%enonthatistrulyduetothequantu%%echanicalnatureoflight,sinceonlyquantu% %echanicscouldprovideaconsistente(planationoftheobservedresults. Shortlyafterthise(peri%ent,scientistsstartedplayingwithittoillustrateandverifyallthe strangethingstaughtinele%entaryquantu%%echanicscourses,%anyofwhichhadre%ainedfor allthesedecadesasunchec,edarticlesoffaith.Beyondtheantibunchinge4ect,ani%portantgoal was to generate a “single photon state”, that is the 9rst e(cited state of the quanti+ed radiation 9eld,containingonlyonequantu%ofenergy.Suchstateswereproducedsi%ultaneouslyin19H6in

RochesterbyEhungLiHongandLeonardMandel[H],andinOrsaybyPhilippeGrangier,GM erard Roger and Alain Aspect [9], by using light sources which e%it pairs of photons. The detection of the9rstphotoninthepair“heralds”thesecondone,andatthatinstanttheelectro%agnetic9eld is prepared in a “single photon state”. For an ideal single photon state, the probability of Coint detectiononbothsidesofthebea%splitterisstrictly+ero-thephotondoesnotsplit2see9g.23. Inaddition,theOrsaytea%setouttoillustratethe wave-particledualityofquantu%%echanics.

Theyreasonedthatthephotonbehavesli,eaparticlebecause,bydeter%iningwhichdetectorgot activated, we are actually answering a particle-li,e question, na%ely “which way did the photon go when it hit the bea%splitter ?” But by putting a second half-silvered %irror to %a,e a Mach- Nehnder interfero%eter 29g. 23 they could see the interference of the two paths that the single photoncouldta,e,thusbringingintoevidenceitswave-li,enature.Inotherwords,bynottrying toanswerthequestionofwhichwaythephotonwent,theyallowedittogo both ways atonceand produceaninterferencepattern,Custli,eanywavewoulddo. 3 Using

single photons : Quantum Key Distribution Inthe%eanti%e,scientistsstartedthin,ingofhowtoe(ploitthequantu%propertiesofthephoton todousefulthings.Trans%ittinginfor%ationbycodingitonatrainofsinglephotonsisnotsuch
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P. Grangier S eminaire Poincar 1 photon 1 photon Figure2:Wave-particledualityforasinglephoton:Aone-photonstateofthelightispreparedand senttowardsabea%splitter.Intheleftpartofthe9gure,thesinglephotone(hibitsaparticle-li,e behaviour : it is detected by either one of the detectors, but there is never a “double clic,”. One would conclude classically that the photon “chooses

its way” on the bea%splitter. In the right part of the 9gure, the output bea%s are reco%bined to for% a Mach-Nehnder interfero%eter. For a single-photon input, the photon output channel can now be controlled by %oving any of the two %irrors 2double arrows on the 9gure3 : for instance, one can adCust the %irror8s position so thatthephotonalwaysgoestotheupperchannel2withprobabilityone3.Thisisthesingle-photon equivalentofhavingatotallydestructiveinterferenceinthelowerchannel2“real”fringescanalso be reconstructed by sending %any individual photons, for various %irrors positions3. Elassically,

onewouldconcludethateachphotonhastogothroughbothwaysli,ea wave,but thisconclusion iscontradictorywiththepreviousone.Onlythequantu%theoryoflightisabletogiveaconsistent descriptionofbothe(peri%ents. a good idea, since trans%ission losses would produce rando% deletions of photons, thus %a,ing any predeter%ined %essage unintelligible. However, a rando% nu%ber does not su4er fro% this disadvantage,sinceitre%ainsrando%2butnotthesa%e3afterarando%deci%ationofitsdigits. And rando% nu%bers constitute a valuable resource, because they cannot be guessed and can

thereforebeusedascryptographic,eystoencode%essagesforsubsequentsecuretrans%ission.In 19H5,EharlesBennettandGillesBrassardproposedaprotocol[10]2,nownasBBH53,forsendinga rando%nu%berusingatrainofsinglephotons.Thisturnedouttobeaveryfruitfulideathatgave birthtoanewresearch9eld,oftencalled“quantu%cryptography”,or%oretechnically“quantu% ,ey distribution” 2QLD3. Over the years, a large nu%ber of groups e(plored both the theoretical ande(peri%entalsidesoftheseideas.ThesecurityproofsofQLDbeca%e%oreand%orepowerful andgeneral,whilehardwarei%ple%entationsofQLDsyste%s%adeconsiderableprogress.

TheBBH5protocolforsendingarando%sequenceofbitsper%itstheauthori+edusers2often na%ed Alice and Bob3 to detect any attac, in which an eavesdropper 2usually called Eve3 tries to intercept the ,ey, for instance by %easuring each photon and then re-e%itting it so as not to interrupt the trans%ission. The security of the trans%ission is unconditionally guaranteed by a strategy based on the quantu% theory of %easure%ent and the use of superposition states. For thatpurpose,thebitsarecodedbyestablishinganon-uniquecorrespondencebetweenabitvalue and the polari+ation states of the photon. For e(a%ple, the

bit values 0 or 1 %ay be coded by e%itting a photon polari+ed along P or along P respectively 29g. 33. Alternatively, the “diagonal basis %ay be used to encode 0 and 1 by polari+ing the photon along P or P respectively. We %ay re%ar,,however,thatsincethetwobasesarenotorthogonaltoeachother,ade9nitebitvaluein oneofthe%ise(pressedasasuperpositionstateintheother,fore(a%ple P G2P QP 2.During thetrans%issionthetwobasesareinterchangedrando%ly,sothatareceiverwhodoesnotusethe sa%e basis as the e%itter will receive a superposition state and thus get erroneous results half of

theti%e.Fore(a%ple,ifa0iscodedbye%ittingaphotonpolari+edalong P butthe%easure%ent is carried out in the diagonal basis, the photon will be detected with equal probability to have a or P polari+ation2thusinterpretedasa0ora1withequalprobability3,producinganerrorhalf of the ti%e. This is not a proble% for Alice and Bob, because after the trans%ission is co%plete
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Vol. 2, 2005 Experiments ith single photons 5 ALICE BOB Quantum channel Classical channel Figure 3: Quantu% Ley Distribution : Using the quantu% channel, Alice sends to Bob a strea% of photons that are individually

polari+ed along any of the four directions P ,P ,P ,P . By agreeing on the %easure%ent basis after Bob has received the photons, and co%paring a subset of the e(changeddatathroughthepublicchannel,AliceandBobcane(tractafullysecuresecret,ey. theycanco%parethebasissetsusedine%issionandreceptionanddiscardtheeventsinwhichthe basis sets were di4erent. When the eavesdropper, however, uses the wrong basis set in the course ofthetrans%ission2andthiswilloccurstatisticallyforhalfofthebitsreceived3shehasnowayof co%paring it with the basis used in e%ission, and thus the errors in her reception %ean that

she retrans%its erroneous data 25S of the ti%e. The legiti%ate users can then detect the presence of the eavesdropper si%ply by co%paring a rando% sa%ple of the bits received to obtain the error rateofthetrans%ission. In practice, there are always trans%ission errors, and %erely interrupting the trans%ission as soon as the error rate increases 2possibly due to Eve, but possibly not3, would not be of great use to Alice and Bob. But a crucial point is that, as long as the error rate is not too large, the authori+edpartiesarealwaysabletoe(tractfro%thee(changedquantu%dataasecret,eythatis

absolutely secure .Thisisobtainedbyusingprovablysecureclassicalalgorith%ictechniques,,nown as“privacya%pli9cation”,thatrelyonsuitablydesignedhashingfunctions.Asaresult,thee4ect of an increase in the error rate will be to decrease the rate of trans%ission of the secret ,ey, but not its security. Obviously, only a 9nite error rate is tolerable, and in practice the secret ,ey rate dropsto+erowhentheerrorrategoesaboveavaluecloseto15S. Presently, several laboratories have de%onstrated the quantu% trans%ission of a crypto-

graphic,eyinoptical9bers,fordistancesupto=0,ilo%etersandtrans%issionratesontheorder of a few ,bitsIs [11]. Such syste%s are now co%%ercially available, fro% co%panies such as “id Quantique” based in Geneva [12]. These devices %ay be relevant for speciali+ed econo%ic niches that require absolute security over concentrated areas, li,e business or %anage%ent centers, and that are not too sensitive to cost and infrastructure co%ple(ity. There has also been proposals to i%ple%entglobal,eydistributionbyusingsatellite-borneQLD. Research on quantu% ,ey distribution has also sti%ulated interesting

technological develop- %ents, in particular in the 9eld of single photon detectors. Silicon avalanche photodiodes 2APD3 are sensitive enough to detect single photons in the visible and near-infrared range, and have found uses in %any 9elds, for instance in single-%olecule detection for biological applications. In the window of %ini%al attenuation in optical 9bers 21550 n%3 which is interesting for long distance teleco% trans%issions, QLD applications have pushed forward the develop%ent of In- GaAs APDs, and although their perfor%ance does not %atch yet that of silicon APDs, co%plete

photon-counting devices are now co%%ercially available. QLD has also sti%ulated technological progressinotherdo%ains,suchasnon-linearoptics2e.g.high-eTciencypara%etric.uorescencein periodicallypoledwaveguides3,andsoftware2suchasthefull-si+equantu%cryptographysoftware “QUERUPT”designedbyLouisSalvail,andnowpubliclyavailable[13]3.
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P. Grangier S eminaire Poincar Figure 5: Electron %icrograph of a GaAs %icro-post cavity. The photons are e%itted by an InAs quantu%dot2depictedsche%aticallybyatriangle3e%beddedinthecenterofthe%icrocavity,and resonant with the funda%ental cavity %ode.

These photons will be channeled preferentially into that%ode,andthusproduceahighlydirectionalbea%2i%age:I+oAbra%,LPNMarcoussis3. 4 Single photon sources A research area on which QLD has had a particularly deep i%pact is the develop%ent of novel lightsources.Todate,%ostofthepracticalreali+ationsofQLDhavereliedonstronglyattenuated laserpulses,withanaveragenu%berofphotonsperpulse%uchs%allerthanone.Butinthatcase thePoissonphotonstatisticsoflaserlighti%posestwounwantedconsequences:9rst,afractionof the pulses contain two or %ore photons, and this is an open door to infor%ation lea,age towards

aneavesdropperVsecond,%ostoftheattenuatedlaserpulsesactuallydonotcontainanyphotons atall,thusresultinginpenali+inglylowtrans%issionrates.Elearly,aneTcientsourceabletoe%it one,andonlyone,photonineachlightpulsewouldconsiderablyi%provetheperfor%anceofQLD syste%s, especially in high-loss situations, such as satellite co%%unications. The need for such lightsources,co%binedwiththe%orefunda%entalinterestsofacade%iclaboratories-i%proving ourunderstandingand%asteringofquantu%optics-havegivenastrongi%petustoresearchfor sources capable of e%itting single photons “on de%and”, and a great variety of

approaches have beenproposedandi%ple%entedinrecentyears[15]. AttheheartofallsinglephotonsourcesliesasinglenanoscopicobCect,whichiss%allenough so that a transition between its electronic states corresponds to light e%ission fro% a single Such is the case, for e(a%ple, of an ato%, a %olecule or a se%iconductor nano-aggregate. If such an e%itting dipole is brought to an e(cited state, then fro% the %ere conservation of energy it will e%itoneonlyphoton.Ingeneral,spontaneousphotone%issioncanoccurinanydirection,andthus

usuallyonlyaverys%allfractionwillgoinadirectionwhereitcanbeuseful,%a,ingthee%itter very ineTcient. To increase eTciency, the nanoscopic e%itter can be e%bedded in a high 9nesse optical cavity whose di%ensions are of the order of the optical wavelength, that is a few hundred nano%eters.MicroscopicopticalcavitiesaresubCectto“EavityQuantu%Electrodyna%ics”e4ects in which the structure of the electro%agnetic 9eld and the spontaneous e%ission are %odi9ed. In particular, in the so-called “Purcell e4ect”, spontaneous e%ission into the cavity %odes can be

greatlyenhanced,sothat%oste%ittedphotonsarefunneledinoneparticulardirectionandthus generate a highly directional output bea%. In addition, a “user-friendly” single photon source should preferably wor, at roo% te%perature, it should have a high quantu% eTciency, and it shouldbeabletoachieveahighpulserepetitionratewithoutblin,ingorburningout. Suchsinglephotonsourceswereachieved9rstbyusingsingle%olecules,suchasasterrylene e%beddedinacrystalofpara-terphenyl,whichwasused9rstatcryogenicte%peratures,andthen atroo%te%perature.Othercandidates,suchasrhoda%inesorcyanines,havealsobeenidenti9ed, but a

signi9cant drawbac, of %olecules at roo% te%perature is that they irreversibly turn o4 afterso%eirradiationti%e.Thee(act%echanis%reponsibleforthisphotobleachingisstillunder investigation,andi%prove%ents%ayoccurinthefuture. Anotherwell-e(ploredsyste%,studiedbothintheUnitedStatesandinEurope,isthesingle
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Vol. 2, 2005 Experiments ith single photons 7 self-asse%bled se%iconductor quantu% dot, consisting of an InAs nano-aggregate e%bedded in GaAs.Thesinglephotonthatise%ittedwhenoneelectronholepairisinCectedinthequantu%dot caneasilybeidenti9edthan,stoits

wavelength.Inaddition,inviewof%a(i%i+ingthecollection eTciency of the single photon that is e%itted, the InAs quantu% dots can easily be incorporated ina%icrocavity29g.53%adeofse%iconductorthroughthestandardprocessingtechnologiesused for %icroelectronics. In such syste%s, cavity-enhanced spontaneous e%ission 2Purcell e4ect3 has beenobservede(peri%entallytobefasterthaninfreespacebyafactorofupto20,whilefactorsof severalhundredshouldbepossibleaccordingtotheory.Presently,quantu%dotsoperationrequires liquidheliu%te%peratures,butthisshouldi%proveinforthco%ingyears.

Anotheravenueisusingindividualnitrogen-vacancy2NW3colorcentersindia%ond.TheNW centershave%anysi%ilaritieswith%oleculesbutaree(tre%elyphotostable,evenatroo%te%per- ature. Another advantage is that they appear both in bul, dia%ond or in dia%ond nanocrystals, and are therefore easy to %anipulate 29g. 13. A stable source e%itting single photon pulse trains basedonanNWcenterinadia%ondnanocrystale(citedbyas%allsolid-statelaserwasrecently i%ple%ented in Orsay [15]. The overall syste% is a reasonably co%pact, all-solid-state set-up op-

eratingatroo%te%perature,thatisprobablythesi%plestsingle-photonsourcedevelopedsofar. Using this co%pact source delivering trains of single-photon pulses, Ale(ios Beveratos and his colleagues were able to de%onstrate a co%plete quantu% ,ey distribution sche%e [15, 15], where the rate of pulses containing two photons is strongly reduced with respect to an attenuated laser 2by a factor 15 for the sa%e rate of one-photon pulses3. This %a,es interception by the so-called “two-photon attac,s” virtually i%possible. The cryptographic e(change is then %ore robust with respect to on-line losses,

providing a clear advantage over an attenuated laser source for QLD applications. The perfor%ance of this set-up should i%prove further in a near future, providing a highly eTcient, easy to use, and reliable single photon source that would constitute a basic piece ofhardwareforpracticalquantu%,eydistribution2see9g.53. Another way to avoid two-photon attac,s is to use the tric, of “heralded” single photons, that was used in 19H6 to produce single-photon states as said above. In the conte(t of quantu% cryptography,thee(peri%entwasreali+ede.g.inGeneva,byusingpairsoftwinphotons,generated by a

nonlinear optical process called “para%etric downconversion”, so that one %e%ber of the pairheraldsitstwin.Thequantu%%echanical“entangle%ent”thate(istsbetweenthetwinswas also e(ploited with success. Though these sche%es produce photons at irregular intervals, with e4ectivecountingratesthataresubCecttovarioustechnicalli%itations,theydoprovidealsoquite interestingQLDsche%es[11]. Finally,sche%esbasedonsingletrappedato%sorionsinhigh-9nessecavitiesareclearly%ore co%ple( to i%ple%ent, but %ight produce single photons with interesting spectral properties, as

discussedinthesectionbelow.State-of-the-artresultswereobtainedbydroppingortrappingcold ato%s through a high-9nesse cavity : when going through the cavity each ato% e%its a burst of single-photon pulses. Each photon e%ission is triggered by a sequence of laser pulses, including e(citation, e%ission in the cavity %ode, and repu%ping to the initial level. Several recent results alongtheselinesaredescribedinref.[15]. 5 Coalescing photons Loo,ing further to the future, several recent proposals for all-optical quantu% photonic networ,s have been advanced recently based on indistinguishable single

photons acting as .ying qubits, carrying infor%ation fro% node to node and interacting with each other. These ideas can even bee(tendedtowardsthereali+ationofafull-.edgedquantu%co%puter,usingasche%ethatwas proposedrecentlybyE%%anuelLnill,Ray%ondLa.a%%eandGeraldMilburn.Forsuchsche%es towor,,photons%ustbeindistinguishable,thatisthey%ustbeinthesa%e“single%odeofthe electro%agnetic9eld”.Inshouldbenotedthat%ostofthesingle-photonsourcesdescribedabove producephotonsthatareincoherentlyspreadover%any%odesoftheradiation9eldand,although

theyareusableinQLD,theydonothavetheappropriatepropertiesforquantu%co%putation. In order to illustrate what is speci9c to indistinguishable photons, let us consider 9g. 62a3 : Twophotonsaresentontoabea%splitter,insuchawaythatwhenonephotonistrans%itteditends
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P. Grangier S eminaire Poincar Alice Alice Bob Bob 1001 011101110111 000110 010110 010 1001 011101110111 000110 010110 010 Quantum Communication 1001 011101110111 000110 010110 010 1001 011101110111 000110 010110 010 Parity bits ex change Error corr ection Error corr ection Error rate % 1.7 % 101100101100 101100101100

Privacy amplification Privacy amplification Secret Key 16000 bits /s) Hasching function Laser Single Photon 10 Figure 5: Quantu% ,ey e(change with a single photon source, obtained by e(citing dia%ond nanocrystalsbyapulsedlaser.Theupperlefti%ageshowslighte%issionbythedia%ondnanocrys- tals2brightspotsonthei%age3.Theupperrightphotographshowsthee(peri%entalset-up,where the photons are sent though a window to Bob8s detection apparatus, located in another building. The lower part of the 9gure shows the various steps of the protocol which is used to e(tract the 9nalsecret,ey.
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Vol. 2,

2005 Experiments ith single photons 9 0 ! (a) (b) (c) Figure 6: Eoalescing photons on a bea%splitter : When two “single %ode” 2but otherwise inde- pendent3 photons enter a 50-50 bea%splitter 2a3, they %ay be trans%itted or re.ected in various ways,asshownin2b3.Inparticular,bothphotons%aybetrans%itted,orboth%aybere.ected, and it happens that the corresponding probability a%plitudes cancel out. Then the two photons %ustgotothesa%eoutputbea%,asshownin2c3:they“coalesce”onthebea%splitter. upine(actlythesa%e%odeastheotherphotonwhichisre.ected.Thefourpossiblecon9gurations

forthetwophotonsbeingtrans%ittedorre.ectedaredepictedin9g.62b3.Asitisusualinquantu% %echanics, a probability a%plitude in attached to each of these con9gurations, and it turns out that the a%plitudes of the two diagra%s in the %iddle of 9g. 62b3 2both corresponding to one photon in each of the two output ports of the bea%splitter3 have opposite signs. Elearly, if the twophotonsareindistinguishable2havinge(actlythesa%efrequency,direction,andpolari+ation3 the two diagra%s are identical and, since their a%plitudes are of opposite sign, they cancel each other outB The i%%ediate consequence of the

two surviving diagra%s is that the two photons %ust go to the sa%e output bea% : They “coalesce” as they %eet on the bea%splitter to for% a “two-photon state”, that is the second e(cited energy state of the corresponding %ode of the quanti+edelectro%agnetic9eld.Thissurprisingquantu%interferencee4ectwas9rstpredictedand observedin19H=,byLeonardMandelandcowor,ers.Theyusedactuallypairsof“twinphotons”, si%ultaneously produced in para%etric down-conversion, so it was possible to argue that the two photons ,new about each other before, since they were “twins” e%itted in a single para%etric

.uorescenceevent.Woulditbepossibletogetthesa%ee4ectbyusingtrulyindependentlye%itted 2albeitindistinguishable3photons?Thequantu%answertothisquestionisyes,anditisnotpure rhetoric,becauseinterferencebetweenindependentlye%ittedphotonsisactuallywhatisrequired forapplicationsinquantu%infor%ationprocessing,usingtheLnill-La.a%%e-Milburnsche%e. Thecoalescenceoftwoindistinguishablebutindependentlygeneratedphotons,fro%asource consisting of a single quantu% dot in a se%iconductor %icrocavity, was e(peri%entally de%on- strated very recently in Stanford [16]. This e(peri%ent can be seen as a 9rst step

towards the reali+ation of conditional quantu% logic gates that would %a,e photon-based quantu% co%put- ing possible. But diTculties should not be underesti%ated : with present-day setups the error rates would be by orders of %agnitude too large, co%pared with the range where quantu% error- correcting codes can play an eTcient role. Also, the nu%ber of interfering photons required to i%ple%ent a useful co%putation is huge, and the integration of the devices would have to be pushedwellbeyondthepresenttechnologicalcapabilities. 6 “En guise de conclusion” : towards entangled photons on demand

Photon pairs e%itted in para%etric downconversion have often been %entioned above, because they have %any applications in quantu% optics : conditional preparation of single photon states, quantu% ,ey distribution, and last but not least, they can be prepared in an entangled state. When two photons are entangled, their states are always correlated no %atter how we choose to %easure the%, as if the two photons constituted a single quantu% obCect. For instance, a pair of
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10 P. Grangier S eminaire Poincar polari+ation-entangled photons will e(hibit correlations in every possible

polari+ation basis, and perfor%ing polari+ation correlation %easure%ents on the two photons once they are far apart leadstoaviolationofBell8sinequalities.This%eansthatthecorrelationsthatappearbetweenthe resultsofthepolari+ation%easure%entsonthetwore%otephotonsaresostrong,thatnoclassical %odelbasedon“localrealis%”isabletoe(plainthe%.Inquantu%infor%ationprocessing,sucha quantu%entangle%entisa“resource”,becauseitcannotbecreatedbylocalactionsontwore%ote photons, and it allows one to perfor% so%e speci9c tas,s, such as quantu% teleportation of the

2un,nown3polari+ationstateofathirdphoton.Entangledphotonpairsalsoprovideawaytowards the so-called “quantu% repeaters”, that would allow one to develop quantu% ,ey distribution sche%esoverarbitrarilylongdistances2itisnoticeablethat“classicalrepeaters”,co%%onlyused inopticalteleco%%unication,donotpreservethequantu%cryptographicsecurity3. Presently,the%ainsourceofentangledphotonpairsarepara%etric.uorescenceevents,but these events are essentially rando%, so that the pair production process obeys Poisson statistics.

Inthesa%ewayasdeter%inisticsinglephotongenerationisuseful,deter%inisticpairproduction would allow new quantu% co%%unication protocols to be developed. How can this be achieved? One %ay si%ply try to i%prove upon the old idea of the radiative cascade, that was used in the =08s and H08s for perfor%ing e(peri%ental tests of Bell8s inequalities. But instead of using %any- ato%sourcesasitwasdoneatthatti%e,oneshoulduseatwo-photonradiativecascadeofasingle e%itter.Severalgroupshaveshownthataquantu%dotdoesdisplaysuchacascade,corresponding

totheradiativetransitionsbetweentheelectronicstatesofthequantu%dotcontainingtwo,one,or +eroelectron-holepairs.However,the9rste(peri%entsdidnotproducetheresultshopedfor:The photonse(hibitedcorrelationsonlyforonepolari+ationbasis.Inotherwords,theywerecorrelated asiftheywereclassicalobCects,andwerenotentangledquantu%%echanically,because,apparently, decoherence processes in the quantu% dot rapidly destroy the entangle%ent. E(ploitation of the Purcell e4ect to reduce the radiative lifeti%e beyond the decoherence ti%e should, in principle, per%ittheproductionofentangledphotonpairs“onde%and”.

Whilethelong-ter%goalofbuildingaquantu%co%puterisfar-fetched,a%ediu%-ter%goal for these e(peri%ents is to develop long-distance quantu% co%%unication networ,s, that would allow for the i%ple%entation of QLD syste%s over arbitrary large distances. One %ay thin, also about %ore elaborate protocols, able to share a quantu% secret between %any 2rather than two3 users. Such things are presently still far fro% being i%ple%ented, but this is one very fascinating aspectsofquantu%infor%ation:bye(ploitingthestrangestpropertiesofsinglephotonsandsingle

ato%s,itallowsusto%ovecontinuouslyfro%sciencetoscience-9ction,andbac,. References [1] This article and the following ones are translated in french in “Albert Einstein : Quanta”, by F.Balibar,O.DarrigolandB.Jech, EditionsduSeuil,Paris,19H9. A.Einstein, Uber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt ,AnnalenderPhysi,, 34 ,591219053. [2] A.Einstein, Uber die Entwicklung unserer Anschauungen uber das Wesen und die Konstitution des trahlung ,Physi,alischeNeitschrift 10 ,H1=219093 [3] A.Einstein, Zum gegenw artigen tand des trahlungsproblems

,Physi,alischeNeitschrift 10 ,1H5 219093 [5] A.Einstein, Quantentheorie des idealen gases ,PreussischeA,ade%iedesWissenschaften,Phys.- %ath.Llasse,Sit+ungberichte,1H219253. [5] W.E. La%b and M.O. Scully, The Photoelectric Effect Without Photons , in “Polarisation, MatiX ereetRayonne%ent”,ed.A.Lastler,PressesUniversitairesdeFrance,363-369219693. [6] J. F. Elauser, Experimental Distinction Between the Quantum and Classical Field Theoretical Predictions for the Photoelectric Effect ,Phys.Rev.D ,H5219=53.
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Vol. 2, 2005 Experiments ith single photons 11 [=] H. J.

Li%ble, M. Dagenais, and L. Mandel, Photon antibunching in resonance fluorescence Phys.Rev.Lett. 39 ,691219==3. [H] E.L.HongandL.Mandel, Experimental realization of a localized one-photon state ,Phys.Rev. Lett. 56 ,5H-60219H63. [9] P.Grangier,G.RogerandA.Aspect, Experimental evidence for a photon anticorrelation effect on a beam-splitte r : a new light on single-photon interferences ,EurophysicsLett. ,1=3219H63. [10] E.H. Bennett and G. Brassard, Int. Eonf. Eo%puters, Syste%s and Signal Processing, Ban- galore,India,1=5219H53. [11] A review on quantu% cryptography %ay be found in :

N. Gisin, G. Ribordy, W. Tittel, and H.Nbinden, Quantum cryptography ,Rev.Mod.Phys. .4 ,155220023. [12] idQuantiqueSA,http:IIwww.idquantique.co% [13] http:IIwww.c,i.au.d,Ie(peri%entIqryptoIdocI [15] Manye(peri%entalresultsonsinglephotonspulsescanbefoundinthreespecialissues: “Quantu% interference and cryptographic ,eys : novel physics and advancing technologies 2QUIEL3”,inTheEuropeanPhysicalJournalD 18 2232February20023,editedbyP.Grangier, J.G.RarityandA.LarlssonV “Proceedings of the Tenth International Eonference on Modulated Se%iconductor Structures 2MSS103”,inPhysicaE, 13

22-532March20023,editedbyG.BauerV “Focus on Single Photons on De%and”, in New Journal of Physics 220053, edited by P. Grangier, B. Sanders and J. Wu,ovic 2free access at http:IIwww.iop.orgIEJIabstractI136=- 2630I6I1IE053. [15] A.Beveratos et al ., ingle photon quantum cryptography ,Phys.Rev.Lett. 89 ,1H=901220023V [16] E.Santori et al ., Indistinguishable photons from a single-photon device ,Nature 419 ,595220023.