Institut d’optique - 10 mai 2005

Jean-François RochLaboratoire de Photonique Quantique et Moléculaire,Ecole Normale Supérieure de Cachan

roch@physique.ens-cachan.fr

Merci à Philippe Grangier et Alain Aspect (Laboratoire Charles Fabry, Institut d’Optique)

Impulsions à un photon

2

La lumière à travers les âges

•! Newton (Opticks, 1702): particules (couleurs diverses)

•Antiquité (Égypte, Grèce): particules vers l’œil ou depuis l’œil (Epicure, Aristote, Euclide)

Moyen âge, renaissance: ingénierie: lunettes correctrices, lunette astronomique (Al Hazen, Bacon, Leonard de Vinci, Galilée, Tycho…)

XVIIème siècle: Ondes (analogie « ronds dans l’eau »): Huyghens

3

XIXe siècle. Le triomphe du modèle ondulatoire

Young, Fresnel (1822): interférence, diffraction, polarisation

Maxwell (1870): la lumière est une onde électro magnétique

1900: « La fin de la physique» (Lord Rayleigh) … mis à part deux détails!

4

Début XXe: Les photons (le retour des particules)

•! Einstein (1905). Lumière constituée de quantas, grains élémentaires d’énergie E=hv et d’impulsionp= hv/c (baptisés « photons » en 1922)."Prédictions quantitatives pour l’effet

photoélectrique

Comment réconcilier le modèle corpusculaire avec les phénomènes de diffraction, interférence, polarisation? Onde ou particule?

Idées mal acceptées jusqu’aux travaux expérimentaux de Millikan (1915, effet photoélectrique).Einstein prix Nobel (1922) pour l’effet photoélectrique

5

Facile à énoncer, mais très difficile à se représenter par des images issues du monde accessible à nos sens.

La dualité onde-particule (Louis de Broglie, 1925)

La lumière est à la fois une onde (capable d’interférer, d’être diffractée) et un ensemble de particules possédant une énergie, une quantité de mouvement…

… et de même les particules comme les électrons se comportent aussi comme des ondes (diffraction, interférences).

Wave particle duality in textbookswave-like behaviour for particles

6

S

Particles emitted one at a time, all “in the same state” (same origin, direction distribution, energy)

Young’s double slit

D

H2

Detection probability

PD

PD

When detector D moves, PD is modulated

H1

Interpretation: each particle is described by a wave passing through both holes and recombining on the detector.

PD depends on the path difference Δ = SH1D – SH2D

When a hole is closed no modulation (PD constant)

Wave particle duality in textbooksparticle-like behaviour

7

D1

H2

H1

D2

Singles detection P1

Coincidences detection

PC

Singles detection P2

S

D1 et D2 observe random pulses, with a constant mean rate, but no coincidence (PC = 0): anticorrelation

Interpretation: a single particle passes either through H1, or through

H2, not through both holes simultaneously.

A single particle cannot be split.

Particles emitted one at a time, all “in the same state” (same origin, direction distribution, energy)

8

Test du comportement corpusculaire?

D1

H2

H1

D2

Détection simple P1 ≠ 0

Détection en coïncidence

PC = 0

Détection simple P2 ≠ 0

S

Particules émises une par une

Expérience pas faite ainsi jusqu’en 1985•! Caractère corpusculaire « évident » pour électrons, neutrons,

atomes, molécules: observation d’effets ondulatoires•! Lumière très atténuée: distance moyenne entre photons grande

devant dimension de l’interféromètre: observation d’effets ondulatoires en lumière très atténuée

Expérience de Taylor (1909)

9

fente

épingle

figure de diffraction

film

Proceedings of the Cambridgephilosophical society. 15 114-115(1909)

10

Comportement ondulatoire avec lumière très atténuée

Taylor 1906 Diffraction Plaque photo Oui

Dempster & Batho 1927 Réseau, Fabry-Perot Plaque photo Oui

Janossy and Naray 1957 Interféro. de Michelson Photomultiplicateur Oui

Griffiths 1963 Fentes d’Young Intensificateur Oui

Dontsov & Baz 1967 Fabry-Perot Intensificateur NON

Scarl et al. 1968 Fentes d’Young Photomultiplicateur Oui

Reynolds et al. 1969 Fabry-Perot Intensificateur Oui

Bozec et al. 1969 Fabry-Perot Plaque photo Oui

Grishaev et al. 1971 Interféro. de Jamin Intensificateur Oui

Zajonc et al. 1984 Interféro. à fibre; choix retardé

Photomultiplicateur Oui

Alley et al. 1985 Interféro. à fibre; choix retardé

Photomultiplicateur Oui

Comportement ondulatoire

Une question réglée ?

11

Remise en cause du caractère corpusculaire de la lumière très atténuée

Propriétés de l’effet photoélectrique parfaitement interprétées par le modèle semi-classique de la photodétection (1964)

•!Détecteur quantique (atome, molécule, solide conducteur, …)•! Lumière : onde électromagnétique classique

NB: en 1905 (huit ans avant l’atome de Bohr) pas de description quantique, ni pour la matière, ni pour la lumière: effet photoélectrique incompréhensible dans le cadre classique. Einstein a choisi de quantifier la lumière. Il aurait pu choisir de quantifier la matière.

La lumière très atténuée présente-t-elle un comportement corpusculaire?Comment caractériser quantitativement un comportement corpusculaire?

Criterion for particle-like behaviour

12

D1

H2

H1

D2

Singles detection P1 ≠ 0

Coincidences detection

PC

Singles detection P2 ≠ 0

S

α =PC

P1 × P2

= 1

α =PC

P1 × P2

< 1

Particle: one expects Pc = 0

Wave: passes through both holes:One expects Pc ≠ 0

More precisely, semi-classical model for a wave

Criterion for particle-like behaviour:

P. Grangier, G. Roger, and A. Aspect, Europhys. Lett. 1, 173 (1986)

13

La lumière très atténuée n’a pas un comportement de particules (Aspect + Grangier, 1985)

Impulsions émises par une diode électroluminescente et très atténuées: 0,01 photon par impulsion, en moyenne

Résultat expérimental: αmeas = 1.07 ± 0.08 Comportement ondulatoire

En accord avec les prédictions de la théorie quantique de la lumière. La lumière très atténuée est décrite comme un état quasi-classique.

Sources de photons uniques

Dans les sources lumineuses classiques (lampe fluorescente, laser, LED, ...) un très grand nombre d’émetteurs sont excités simultanément.Comment isoler un seul atome (ou émetteur excité) ?

atome isoléexcité

émet un photon et un seul (g)

(e)

|1〉

La théorie quantique de la lumière permet de concevoir des sources de photons uniques pour lesquels on prévoit un comportement corpusculaire :

PC = 0et

α =1

The first single-photon sourceAlain Aspect et Philippe Grangier - 1986

Atomic radiative cascade. Single atom isolated temporally : after a time duration of 5 ns following detection of ν1 a single atom is ready to emit a single photon with ν2 frequency.

P. Grangier, G. Roger, et A. Aspect, Europhys. Lett. 1, 173 (1986)

Résultat expérimental:

αmeas = 0.18 ± 0.06

Anticorrélation (α < 1)

Comportement corpusculaire

Et aujourd’hui ?

• On utilise des atomes ou des ions refroidis et piégés : voir l’exposé suivant d’Antoine Browaeys

• Il s’agit cependant de sources complexes à mettre en œuvre (voir la visite des laboratoires !)

• Peut-on imaginer des sources de photons uniques plus “pratiques” ?

Single photon from twin photons

Scheme suitable for efficient generation of photon pairs using nonlinear waveguide structures with QPM χ(2)

parametric fluorescence in nonlinear crystals(L. Mandel, J. Rarity, A. Zeilinger, N. Gisin, H. Weinfürter, P. Kwiat, …)

Nonlinearcrystal

Pump532 nm

Idler photon810 nm

Signal photon 1.55 μm (telecom)

!kpump = !ksignal + !kidler

1

λpump=

1

λsignal+

1

λidler

18

Emission de lumière par un atome

NiveauxatomiquesdiscretsExcitation

décharge électriqueabsorption de lumière

Emissionspontanée

niveau excite

energie

niveau fondamentalE0

E1

E2

E3

hν = E1 − E0

19

Fluorescence d’une moléculeniveaux discrets d′energie → bandes d′energie

νabs νfluo

νabs ≥ νfluo

decalage Stokes

τp

excitationimpulsionnelle

→ photon unique

S0

S1

S0

S1

photon

Single photons out of a molecule Dispersed single molecules can be observed using confocal microscopy and can therefore easily produce single photons on demand

δt !1

Γ

Γ

δtS1

S0

Proposal & first experimentF. De Martini et al.Phys. Rev. Lett. 76, 900 (1996)

D’autres sources de photons uniques

InAs quantum dotsin micropillars

(Y. Yamamoto, Izo Abram, J.-M. Gérard, J.-P. Poizat)

CdSe nanocrystals (J.-P. Hermier)Narrow spectrum related to the size

NV colored centers of diamond "artificial molecule" perfectly photostable at room T

Molécules : souplesse d’emploi,

efficacité élevée,mais photoblanchissent.

80

60

40

20

0

Inte

nsity

(kHz

)

2520151050Time (s)

bin=2ms

NV colour centre in diamond

V

N

C

substitutional nitrogen atom (N) and a vacancy (V) in the adjacent lattice site

Absorption

Emission

!

a.u.

637nm 750nm

ZPL

Detection et étude comme objet quantique unique :A. Dräbenstedt, L. Fleury, C. Tietz, F. Jelezko, J. Wrachtrup, C. von Borczyskowski, Science 276, 2012 (1997).Thèse d’Alexios Beveratos (groupe de Philippe Grangier Institut d’Optique): source de photons uniques

Creation of NV colour centres• Nitrogen impurities are naturally presentin synthetic diamond (type I)• Electronic irradiation to create vacancies V in the diamond matrix + annealing at 800°C

€

NV0 + N ↔ N+ + NV-

V

N

C

VN

C

(a)(b)

200

100

0

counts

850800750700650600

wavelength (nm)

(1)(2)

24

Emission dans le diamant massifndiamant = 2.4

100 µm

1.5 mm

Angle limite ~ 24.5°la lumière reste piégée...

Light emission in diamondDiamond nanocrystals instead of bulk crystal

Advantages of nanocrystals : - Higher collection efficiency (no internal reflection)- Less background from host matrix- Easier to handle and well suited for studying the influence of refractive index on emitter’s radiative lifetime

Silica substrate

spacer

Bragg mirror

Polymer host

constructive interference

ndiamond = 2.4

50 nm thickness ! λ0/n

silica nsilica

26

Nanodiamonds (Th. Gacoin, PMC)Powder of synthetic diamond (de Beers, type Ib)size between 0-5 microns

cover platesilica, mirror, etc.

colloidal solution+ size selection

4 steps

dispersed nanoparticlestypical diameter ~ 90 nm

equivalent to a few 10-12 carat = pico-jewelry

spin-coating

CW or PulsedExcitation

Diamondsample

PinholeØ100µ

Filters

Dichroicmirror

z

Spectrometer Delay

Confocal MicroscopePhoton Counting Devices

g(2)(τ)

50/50Beam-splitter

Avalanchephotodiodes

Time -to-Amplitudeconverter

Experimental set-up

(θ, φ)

scanning mirror

metallographic objective

NA = 0.9 10

8

6

4

2

0

µm

1086420

µm

raster scan

10 × 10 µmfluorescence background bleaches after long enough illuminationOnly the color center survives!

@ 532 nm

Single photons from diamond colour centres

1. Single photon “on demand” 2. Single-photon wavefront-splitting interferences 3. Near infrared single-photon emission

OUTLINE

29

Wavefront-splitting of a single photon

Histogram ofcoincidences

StopTACStartMulti

ChannelAnalyzer

S0

S1

APD 1

APD 2

Fresnel’s biprism

30

Correlation parameter

TIA

→ α =

NC × Npulse

NA × NB10−2 photon/pulse

Vincent Jacques et al.: Single photon wavefront-splitting interference : an illustration of the light quantum in action 3

3 “Which-path” experiment : particle-likebehaviour

Single photons emitted by the N-V colour centre are nowsent at normal incidence onto a Fresnel’s biprism. Evi-dence for a particle-like behaviour can be obtained us-ing the arrangement of Fig.1. If light is really made ofquanta, a single photon should either be deviated upwardsor downwards, but should not be split by the biprism. Inthat case, no coincidences corresponding to joint photode-tections on the two output beams should be observed. Onthe opposite, for a semiclassical model that describes lightas a classical wave, the input wavefront will be split intwo equal parts, leading to a non-zero probability of jointdetection on the two photodetectors. Observation of zerocoincidences, corresponding to an anticorrelation effect,would thus give evidence for a particle-like behaviour.

For a realistic experiment aimed at evidencing thisproperty, we need to establish a criterion which enablesus to discriminate between a particle-like behaviour andanother one compatible with the semi-classical model forlight. For that, we faithfully follow the approach intruducedin Ref.[7] for interpreting single photon anticorrelation ef-fect on the two output channels of a beamsplitter. Con-sidering a run corresponding to NT trigger pulses ap-plied to the emitter, with N1 (resp. N2) counts detectedin path 1 (resp. 2) of the interferometer, and NC de-tected coincidences, it is straightforward to show that anysemi-classical theory of light, in which light is treated asa wave and photodetectors are quantized, predicts thatthese numbers of counts should obey the inequality

α =NCNT

N1N2≥ 1 (1)

Violation of this inequality thus gives a criterion whichcharacterizes nonclassical behaviour. For a single photonwavepacket, perfect anticorrelation is predicted since thephoton can only be detected once, leading to α = 0 inagreement with the intuitive image that a single photoncannot be detected simultaneously in the two paths of theinterferometer. On the other hand, inequality (1) cannotbe violated even with faint laser pulses. Indeed, in thiscase the number of photons in the pulse follows a Poissonlaw predicting α = 1. This value indicates that coinci-dences will then be observed preventing the particle-likebehaviour to be evidenced. We measured the α correla-tion parameter for triggered single-photon pulses and forfaint laser pulses. To establish a valid comparison betweenthese two cases, all data have been taken for an identicalmean number of detected photons per pulse, below 10−2.

Since the single-photon source emits light pulses trig-gered by a stable external clock and well separated intime, the value of α can be directly inferred from therecord of all photon arrival times. Every photodetectionevent produced by the two avalanche photodiodes is time-stamped using a time-interval-analyser (TIA) computerboard (GT653, GuideTech). Straightforward processing ofthese timestamps over a discrete time base allows us toreconstruct the number of detection events on each out-put channel of the biprism interferometer, and thus gives

Table 1. Measurements of the correlation parameter α as-sociated to ten sets of 105 photodetections registered for (a)faint laser pulses with a mean number of photons per pulsebelow 10−2 and (b) single-photon pulses emitted by the N-Vcolour centre. As the laser emits coherent states, the numberof photons in each pulse is given by poissonian statistics, lead-ing to a correlation parameter α ≈ 1. On the other hand, ananti-correlation effect, corresponding to α < 1, is clearly ob-served for single-photon pulses propagating through the Fres-nel’s biprism.

(a) Faint laser pulses

Acquisition duration (s) N1 N2 NC α

4.780 49448 50552 269 1.1804.891 49451 50449 212 0.9374.823 49204 50796 211 0.9344.869 49489 50511 196 0.8754.799 49377 50623 223 0.9814.846 49211 50789 221 0.9824.797 49042 50958 232 1.0214.735 49492 50508 248 1.0774.790 49505 50495 248 1.0904.826 49229 50771 219 0.970

(b) Single-photon pulses

Acquisition duration (s) N1 N2 NC α

5.138 49135 50865 28 0.1325.190 49041 50959 23 0.1095.166 49097 50903 23 0.1095.173 49007 50996 28 0.1335.166 48783 51217 29 0.1375.167 48951 51049 31 0.1475.169 49156 50844 30 0.1425.204 49149 50851 32 0.1525.179 49023 50977 26 0.1245.170 48783 51217 26 0.123

an access to the “which-path” information. Furthermore,time intervals between two successive photodetections aredirectly inferred from the timestamps ensemble, so as toestimate if a coincidence has occurred or not for each regis-tered photodetection. However the notion of coincidence ismeaningful only accordingly to a temporal gate: there willbe a coincidence if two detections happen within the samegate. As the radiative lifetime of the emitting N-V colourcentre used for the experiment is approximately equal to45 ns (see Fig.3), we set the gate duration to 100 ns. Sucha value is much smaller than the 436 ns time interval be-tween two successive excitation pulses. It also ensures thatabout 90% of the detected photons are considered for dataanalysis.

Using the results given on Table 1 and simple statisti-cal analysis associated to a 95% confidence interval, we in-fer α = 1.00±0.06 for faint laser pulses and α = 0.13±0.01for single-photon pulses.

Faint laser pulses

Vincent Jacques et al.: Single photon wavefront-splitting interference : an illustration of the light quantum in action 3

3 “Which-path” experiment : particle-likebehaviour

Single photons emitted by the N-V colour centre are nowsent at normal incidence onto a Fresnel’s biprism. Evi-dence for a particle-like behaviour can be obtained us-ing the arrangement of Fig.1. If light is really made ofquanta, a single photon should either be deviated upwardsor downwards, but should not be split by the biprism. Inthat case, no coincidences corresponding to joint photode-tections on the two output beams should be observed. Onthe opposite, for a semiclassical model that describes lightas a classical wave, the input wavefront will be split intwo equal parts, leading to a non-zero probability of jointdetection on the two photodetectors. Observation of zerocoincidences, corresponding to an anticorrelation effect,would thus give evidence for a particle-like behaviour.

For a realistic experiment aimed at evidencing thisproperty, we need to establish a criterion which enablesus to discriminate between a particle-like behaviour andanother one compatible with the semi-classical model forlight. For that, we faithfully follow the approach intruducedin Ref.[7] for interpreting single photon anticorrelation ef-fect on the two output channels of a beamsplitter. Con-sidering a run corresponding to NT trigger pulses ap-plied to the emitter, with N1 (resp. N2) counts detectedin path 1 (resp. 2) of the interferometer, and NC de-tected coincidences, it is straightforward to show that anysemi-classical theory of light, in which light is treated asa wave and photodetectors are quantized, predicts thatthese numbers of counts should obey the inequality

α =NCNT

N1N2≥ 1 (1)

Violation of this inequality thus gives a criterion whichcharacterizes nonclassical behaviour. For a single photonwavepacket, perfect anticorrelation is predicted since thephoton can only be detected once, leading to α = 0 inagreement with the intuitive image that a single photoncannot be detected simultaneously in the two paths of theinterferometer. On the other hand, inequality (1) cannotbe violated even with faint laser pulses. Indeed, in thiscase the number of photons in the pulse follows a Poissonlaw predicting α = 1. This value indicates that coinci-dences will then be observed preventing the particle-likebehaviour to be evidenced. We measured the α correla-tion parameter for triggered single-photon pulses and forfaint laser pulses. To establish a valid comparison betweenthese two cases, all data have been taken for an identicalmean number of detected photons per pulse, below 10−2.

Since the single-photon source emits light pulses trig-gered by a stable external clock and well separated intime, the value of α can be directly inferred from therecord of all photon arrival times. Every photodetectionevent produced by the two avalanche photodiodes is time-stamped using a time-interval-analyser (TIA) computerboard (GT653, GuideTech). Straightforward processing ofthese timestamps over a discrete time base allows us toreconstruct the number of detection events on each out-put channel of the biprism interferometer, and thus gives

Table 1. Measurements of the correlation parameter α as-sociated to ten sets of 105 photodetections registered for (a)faint laser pulses with a mean number of photons per pulsebelow 10−2 and (b) single-photon pulses emitted by the N-Vcolour centre. As the laser emits coherent states, the numberof photons in each pulse is given by poissonian statistics, lead-ing to a correlation parameter α ≈ 1. On the other hand, ananti-correlation effect, corresponding to α < 1, is clearly ob-served for single-photon pulses propagating through the Fres-nel’s biprism.

(a) Faint laser pulses

Acquisition duration (s) N1 N2 NC α

4.780 49448 50552 269 1.1804.891 49451 50449 212 0.9374.823 49204 50796 211 0.9344.869 49489 50511 196 0.8754.799 49377 50623 223 0.9814.846 49211 50789 221 0.9824.797 49042 50958 232 1.0214.735 49492 50508 248 1.0774.790 49505 50495 248 1.0904.826 49229 50771 219 0.970

(b) Single-photon pulses

Acquisition duration (s) N1 N2 NC α

5.138 49135 50865 28 0.1325.190 49041 50959 23 0.1095.166 49097 50903 23 0.1095.173 49007 50996 28 0.1335.166 48783 51217 29 0.1375.167 48951 51049 31 0.1475.169 49156 50844 30 0.1425.204 49149 50851 32 0.1525.179 49023 50977 26 0.1245.170 48783 51217 26 0.123

an access to the “which-path” information. Furthermore,time intervals between two successive photodetections aredirectly inferred from the timestamps ensemble, so as toestimate if a coincidence has occurred or not for each regis-tered photodetection. However the notion of coincidence ismeaningful only accordingly to a temporal gate: there willbe a coincidence if two detections happen within the samegate. As the radiative lifetime of the emitting N-V colourcentre used for the experiment is approximately equal to45 ns (see Fig.3), we set the gate duration to 100 ns. Sucha value is much smaller than the 436 ns time interval be-tween two successive excitation pulses. It also ensures thatabout 90% of the detected photons are considered for dataanalysis.

Using the results given on Table 1 and simple statisti-cal analysis associated to a 95% confidence interval, we in-fer α = 1.00±0.06 for faint laser pulses and α = 0.13±0.01for single-photon pulses.

Single-photon pulses

Vincent Jacques et al.: Single photon wavefront-splitting interference : an illustration of the light quantum in action 3

3 “Which-path” experiment : particle-likebehaviour

Single photons emitted by the N-V colour centre are nowsent at normal incidence onto a Fresnel’s biprism. Evi-dence for a particle-like behaviour can be obtained us-ing the arrangement of Fig.1. If light is really made ofquanta, a single photon should either be deviated upwardsor downwards, but should not be split by the biprism. Inthat case, no coincidences corresponding to joint photode-tections on the two output beams should be observed. Onthe opposite, for a semiclassical model that describes lightas a classical wave, the input wavefront will be split intwo equal parts, leading to a non-zero probability of jointdetection on the two photodetectors. Observation of zerocoincidences, corresponding to an anticorrelation effect,would thus give evidence for a particle-like behaviour.

For a realistic experiment aimed at evidencing thisproperty, we need to establish a criterion which enablesus to discriminate between a particle-like behaviour andanother one compatible with the semi-classical model forlight. For that, we faithfully follow the approach intruducedin Ref.[7] for interpreting single photon anticorrelation ef-fect on the two output channels of a beamsplitter. Con-sidering a run corresponding to NT trigger pulses ap-plied to the emitter, with N1 (resp. N2) counts detectedin path 1 (resp. 2) of the interferometer, and NC de-tected coincidences, it is straightforward to show that anysemi-classical theory of light, in which light is treated asa wave and photodetectors are quantized, predicts thatthese numbers of counts should obey the inequality

α =NCNT

N1N2≥ 1 (1)

Violation of this inequality thus gives a criterion whichcharacterizes nonclassical behaviour. For a single photonwavepacket, perfect anticorrelation is predicted since thephoton can only be detected once, leading to α = 0 inagreement with the intuitive image that a single photoncannot be detected simultaneously in the two paths of theinterferometer. On the other hand, inequality (1) cannotbe violated even with faint laser pulses. Indeed, in thiscase the number of photons in the pulse follows a Poissonlaw predicting α = 1. This value indicates that coinci-dences will then be observed preventing the particle-likebehaviour to be evidenced. We measured the α correla-tion parameter for triggered single-photon pulses and forfaint laser pulses. To establish a valid comparison betweenthese two cases, all data have been taken for an identicalmean number of detected photons per pulse, below 10−2.

Since the single-photon source emits light pulses trig-gered by a stable external clock and well separated intime, the value of α can be directly inferred from therecord of all photon arrival times. Every photodetectionevent produced by the two avalanche photodiodes is time-stamped using a time-interval-analyser (TIA) computerboard (GT653, GuideTech). Straightforward processing ofthese timestamps over a discrete time base allows us toreconstruct the number of detection events on each out-put channel of the biprism interferometer, and thus gives

Table 1. Measurements of the correlation parameter α as-sociated to ten sets of 105 photodetections registered for (a)faint laser pulses with a mean number of photons per pulsebelow 10−2 and (b) single-photon pulses emitted by the N-Vcolour centre. As the laser emits coherent states, the numberof photons in each pulse is given by poissonian statistics, lead-ing to a correlation parameter α ≈ 1. On the other hand, ananti-correlation effect, corresponding to α < 1, is clearly ob-served for single-photon pulses propagating through the Fres-nel’s biprism.

(a) Faint laser pulses

Acquisition duration (s) N1 N2 NC α

4.780 49448 50552 269 1.1804.891 49451 50449 212 0.9374.823 49204 50796 211 0.9344.869 49489 50511 196 0.8754.799 49377 50623 223 0.9814.846 49211 50789 221 0.9824.797 49042 50958 232 1.0214.735 49492 50508 248 1.0774.790 49505 50495 248 1.0904.826 49229 50771 219 0.970

(b) Single-photon pulses

Acquisition duration (s) N1 N2 NC α

5.138 49135 50865 28 0.1325.190 49041 50959 23 0.1095.166 49097 50903 23 0.1095.173 49007 50996 28 0.1335.166 48783 51217 29 0.1375.167 48951 51049 31 0.1475.169 49156 50844 30 0.1425.204 49149 50851 32 0.1525.179 49023 50977 26 0.1245.170 48783 51217 26 0.123

an access to the “which-path” information. Furthermore,time intervals between two successive photodetections aredirectly inferred from the timestamps ensemble, so as toestimate if a coincidence has occurred or not for each regis-tered photodetection. However the notion of coincidence ismeaningful only accordingly to a temporal gate: there willbe a coincidence if two detections happen within the samegate. As the radiative lifetime of the emitting N-V colourcentre used for the experiment is approximately equal to45 ns (see Fig.3), we set the gate duration to 100 ns. Sucha value is much smaller than the 436 ns time interval be-tween two successive excitation pulses. It also ensures thatabout 90% of the detected photons are considered for dataanalysis.

Using the results given on Table 1 and simple statisti-cal analysis associated to a 95% confidence interval, we in-fer α = 1.00±0.06 for faint laser pulses and α = 0.13±0.01for single-photon pulses.

Vincent Jacques et al.: Single photon wavefront-splitting interference : an illustration of the light quantum in action 3

3 “Which-path” experiment : particle-likebehaviour

Single photons emitted by the N-V colour centre are nowsent at normal incidence onto a Fresnel’s biprism. Evi-dence for a particle-like behaviour can be obtained us-ing the arrangement of Fig.1. If light is really made ofquanta, a single photon should either be deviated upwardsor downwards, but should not be split by the biprism. Inthat case, no coincidences corresponding to joint photode-tections on the two output beams should be observed. Onthe opposite, for a semiclassical model that describes lightas a classical wave, the input wavefront will be split intwo equal parts, leading to a non-zero probability of jointdetection on the two photodetectors. Observation of zerocoincidences, corresponding to an anticorrelation effect,would thus give evidence for a particle-like behaviour.

For a realistic experiment aimed at evidencing thisproperty, we need to establish a criterion which enablesus to discriminate between a particle-like behaviour andanother one compatible with the semi-classical model forlight. For that, we faithfully follow the approach intruducedin Ref.[7] for interpreting single photon anticorrelation ef-fect on the two output channels of a beamsplitter. Con-sidering a run corresponding to NT trigger pulses ap-plied to the emitter, with N1 (resp. N2) counts detectedin path 1 (resp. 2) of the interferometer, and NC de-tected coincidences, it is straightforward to show that anysemi-classical theory of light, in which light is treated asa wave and photodetectors are quantized, predicts thatthese numbers of counts should obey the inequality

α =NCNT

N1N2≥ 1 (1)

Violation of this inequality thus gives a criterion whichcharacterizes nonclassical behaviour. For a single photonwavepacket, perfect anticorrelation is predicted since thephoton can only be detected once, leading to α = 0 inagreement with the intuitive image that a single photoncannot be detected simultaneously in the two paths of theinterferometer. On the other hand, inequality (1) cannotbe violated even with faint laser pulses. Indeed, in thiscase the number of photons in the pulse follows a Poissonlaw predicting α = 1. This value indicates that coinci-dences will then be observed preventing the particle-likebehaviour to be evidenced. We measured the α correla-tion parameter for triggered single-photon pulses and forfaint laser pulses. To establish a valid comparison betweenthese two cases, all data have been taken for an identicalmean number of detected photons per pulse, below 10−2.

Since the single-photon source emits light pulses trig-gered by a stable external clock and well separated intime, the value of α can be directly inferred from therecord of all photon arrival times. Every photodetectionevent produced by the two avalanche photodiodes is time-stamped using a time-interval-analyser (TIA) computerboard (GT653, GuideTech). Straightforward processing ofthese timestamps over a discrete time base allows us toreconstruct the number of detection events on each out-put channel of the biprism interferometer, and thus gives

Table 1. Measurements of the correlation parameter α as-sociated to ten sets of 105 photodetections registered for (a)faint laser pulses with a mean number of photons per pulsebelow 10−2 and (b) single-photon pulses emitted by the N-Vcolour centre. As the laser emits coherent states, the numberof photons in each pulse is given by poissonian statistics, lead-ing to a correlation parameter α ≈ 1. On the other hand, ananti-correlation effect, corresponding to α < 1, is clearly ob-served for single-photon pulses propagating through the Fres-nel’s biprism.

(a) Faint laser pulses

Acquisition duration (s) N1 N2 NC α

4.780 49448 50552 269 1.1804.891 49451 50449 212 0.9374.823 49204 50796 211 0.9344.869 49489 50511 196 0.8754.799 49377 50623 223 0.9814.846 49211 50789 221 0.9824.797 49042 50958 232 1.0214.735 49492 50508 248 1.0774.790 49505 50495 248 1.0904.826 49229 50771 219 0.970

(b) Single-photon pulses

Acquisition duration (s) N1 N2 NC α

5.138 49135 50865 28 0.1325.190 49041 50959 23 0.1095.166 49097 50903 23 0.1095.173 49007 50996 28 0.1335.166 48783 51217 29 0.1375.167 48951 51049 31 0.1475.169 49156 50844 30 0.1425.204 49149 50851 32 0.1525.179 49023 50977 26 0.1245.170 48783 51217 26 0.123

an access to the “which-path” information. Furthermore,time intervals between two successive photodetections aredirectly inferred from the timestamps ensemble, so as toestimate if a coincidence has occurred or not for each regis-tered photodetection. However the notion of coincidence ismeaningful only accordingly to a temporal gate: there willbe a coincidence if two detections happen within the samegate. As the radiative lifetime of the emitting N-V colourcentre used for the experiment is approximately equal to45 ns (see Fig.3), we set the gate duration to 100 ns. Sucha value is much smaller than the 436 ns time interval be-tween two successive excitation pulses. It also ensures thatabout 90% of the detected photons are considered for dataanalysis.

Using the results given on Table 1 and simple statisti-cal analysis associated to a 95% confidence interval, we in-fer α = 1.00±0.06 for faint laser pulses and α = 0.13±0.01for single-photon pulses.

Photodetection timestampsGate duration = 100 nsExcitation period = 436 ns

31

Single-photon interference

ICCD

Interferometer with single-photon source at input (α < 1 observed)

Orsay 1985

Unambiguous wave-like behaviour

32

Single-photon interference patterns

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Inte

nsi

ty (

a.u

.)

-1.0 -0.5 0.0 0.5 1.0Distance (mm)

Z = 11 mm simulation data

2.5

2.0

1.5

1.0

0.5

0.0

Inte

nsity

(a.

u.)

-1.0 -0.5 0.0 0.5 1.0Distance (mm)

Z = 98 mm simulation data

Fit using coherent wave propagation in Fresnel’s

diffraction regimefrom classical optics

33

Dualité onde particule: bizarre!

Première expérienceObservation d’un comportement corpusculaire: photon unique passe soit par H1 soit par H2.

Résultat en D dépend de la

différence des chemins

SH1 – SH2

Deuxième expérienceComportement ondulatoire: photon unique passe par les deux trous à la fois.

Même source, même trous ! Incompréhensible avec images habituelles

34

Pour se rassurer: la complémentarité de Bohr

Même source, même trous ! Incompréhensible avec images habituelles

Les deux expériences sont incompatibles. Il faut choisir la question posée au sytème:

•! Par quel trou passe le photon ?

•! Interférence ?On ne peut poser les deux questions à la fois.

Que se passerait-il si on attendait que l’impulsion lumineuse ait dépassé les trous pour choisir l’appareillage ? Expérience « à choix retardé » (Wheeler).

Wheeler’s delayed choice experiment

35

Mach-Zehnder interferometerSPS

with beamsplitter

~ 30 m

SPS

φ

.

Polarisation interferometer

.. .

Séparateur de faisceau

lame λ/2

EOMSéparateur de

polarisation

Vπ

300

200

100

0

Coup

s

850800750700650600Longueur d'onde (nm)

~ 100nm

NV colour center

radiative lifetime ~25ns80% linearly polarised

Bohr’s complementarity

36

The two experiments are incompatible.One must choose the question : which path ? interference ?The two questions cannot be asked simultaneously.Still gives rise to sometimes confuse debates....

Expérience d’Afshar

37http://users.rowan.edu/~afshar/

38

En première conclusion

Les faits expérimentaux nous forcent à accepter la complémentarité entre les interférences et l’information “which path”. Difficile à réconcilier avec les images et la logique issues du monde à notre échelle. Mais, pour se rassurer:

•! Le formalisme de l’optique quantique en rend compte de façon cohérente.

•! La complémentarité de Bohr permet d’éviter les incohérences logiques.

C’est en s’intéressant aux «bizarreries quantiques» qu’on a développé de nouvelles sources de lumière aux propriétés spécifiquement quantiques et qu’a germé l’idée de l’information quantique et de la cryptographie quantique.Voir l’exposé de Philippe Grangier.

Single photons from diamond colour centres

1. Single photon “on demand” 2. Single-photon wavefront-splitting interferences 3. Near infrared narrow-band single-photon emission

OUTLINE

Near infrared emission of colour centres

photoluminescence ~ 800 nmalmost entirely in the

zero phonon line FWHM ~ 1.2 nm

at room temperature

Thin sample of natural diamond (type 2a)Excitation at ~700 nmT. Gaebel et al., New J. Phys. 6, 98 (2004)

Jörg Wrachtrup and Fedor Jelezko (Stuttgart)

Interpretation: colour centre NE8 (Ni-4N)

courtesy Sergei Kilin

5 5

20

30

40

50

60

20

30

40

50

60

x103

cps

µmX Y

Spectrographe

imageur

APD

miroir

dichroïque

diamant

naturel (Type 2a)

(θ, φ)miroir mobile

diode laser (690 nm)

trou de

filtrage

filtre

passe-haut

AP

D

cube

séparateur

50/50

microscope confocal à balayage

mesure des corrélations temporelles

sta

rt

CTA

stop

taux de fluorescence

coups par

seconde

analyseur

multicanal

50/50

filtre

passe-bande

Experimental set-up

9.5

9.0

8.5

8.0

7.5

7.0

µm

8.07.06.0µm

6040200kcoups/s

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

g(2) (τ

)-20 -10 0 10 20

retard (ns)

Observation of single colour centres

Signal/Background ~ 60 Temporal correlations between emitted photons

Typical time-scale τ=1.4 ns

Limitation due to the jitter of Perkin-Elmer Si APDs

~ 300 psExcitation @ 688 nm,

P=8.7 mW

1000

950

900

850

800

750

700

nom

bre

de c

oups

800780760740longueur d'onde (nm)

789 nm

1000

950

900

850

800

750

700

nom

bre

de c

oups

800780760740longueur d'onde (nm)

Raman(758 nm)

750 nm

766 nm

Photoluminescence spectra

FWHM~2 nm

We found emitters with narrow-band photoluminescence, distributed between 750-800 nme.g. the colour centre shown on the previous slides was emitting at 793 nm

ConclusionColour centres in diamond are really turn-key single-photon emittersAll our results have been obtained with unoptimized off-the-shelf materialsDeveloped ultra-pure CVD diamondLithographically written individual defect centresColour centres are paramagnetic: spin structure in their fundamental level (qubit with long coherence time, quantum gates, quantum memories)

Time is ripe to push diamond for quantum technologies !