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across ages: or ? Antiquity (Egypt, Greece): towards or Wave particle duality for a single from the eye (Epicure, Aristotle, Euclid)

photon: from Einstein licht quanten to Middle age, renaissance: Wheeler’s delayed choice experiment engineering: corrective glasses, telescope (Al Hazen, Bacon, Leonardo da Vinci, Galilée, Kepler…) Lausanne, 12 mars 2009 Newton th Alain Aspect XVII cent.: (Opticks, (as 1702): INSTITUT D’OPTIQUE Graduate School “riddles on particles Campus Polytechnique, Palaiseau water”) (of various Huyghens colours) 1 2

XIXth cent. The triumph of waves Early XXth: Photons (particles come back) •Einstein(1905). Light made of quanta, elementary Young, Fresnel (1822): grains of E = h ν and phc= ν / interference, , (named “photons” in 1926 only). polarisation: ¾Quantitative predictions for the light is a transverse wave ¾Ideas not accepted until Millikan’s experiments on photoelectric effect (1915). ¾Nobel award to Einstein (1922) for the Maxwell 1900: “ photoelectric effect (1870): light is completed” ¾Compton’s experiments (1923): momentum is an (Lord of photon in the ray domain electro- Kelvin) … magnetic except for two How to reconcile the particle description with typical wave phenomenon wave details!?? of diffraction, interference, polarisation? Particle or wave? 3 4

Wave particle duality Wave particle duality: fruitful Einstein 1909 Light is both waves (capable to interfere) and an A very successful concept at the root of the revolution: ensemble of particles with defined energy and momentum… • Understanding the structure of , its properties, its ⎛⎞32 interaction with light Blackbody 2 c ρ ⎟ ενρν=+⎜hd⎟ fluctuations ⎝⎠⎜ 8πν 2 ⎟ •Stability of , , solids •Electrical, mechanical, thermal properties Random particles (“”) Random waves (“speckle”) •Spectroscopic properties • Understanding “exotic properties” 1923 •Superfluidity, supraconductivity, BEC Similarly particles such as behave like a • Inventing new devices wave (diffraction, interference) h •, transistor λ = p applied to large ensembles

How does it work for a single particle? See textbooks (e.g. Feynman) Easy to say the words, but difficult to represent by images 5 6

1 Wave particle duality in textbooks Wave-like behavior with faint light? wave-like behaviour for particles Taylor 1909 Diffraction Photographic plate Oui Dempster & Batho 1927 Grating, Fabry-Perot Photographic plate Oui Detection P Trous d’ D Janossy and Naray 1957 Michelson interferom. Photomultiplier Oui Young probability H1 Griffiths 1963 Young slits Intensifier Oui PD D Dontsov & Baz 1967 Fabry-Perot Intensifier NON S Scarl et al. 1968 Young slits Photomultiplier Oui H Reynolds et al. 1969 Fabry-Perot Intensifier Oui Particles emitted one at a time, 2 Bozec, Imbert et al. 1969 Fabry-Perot Photographic plate Oui all “in the same state” (same When detector origin, direction distribution, Grishaev et al. 1971 Jamin interferometer Intensifier Oui D moves, PD is modulated energy) Zajonc et al. 1984 Fiber interferometer, Photomultiplier Oui When a hole is closed delayed choice

no modulation (PD constant) Alley et al. 1985 Fiber interferometer, Photomultiplier Oui delayed choice Interpretation: each particle is described by a wave passing through both holes and recombining on the detector. Average distance between photons Single particle interference? 7 large compared to interferometer size 8 PD depends on the path difference Δ = SH1D – SH2D

How to know one has single particles? The which path GedankenExperiment The “which path” Gedankenexperiment Singles detection P ≠ 0 H 1 Singles detection Particles 1 D Particles emitted 1 P1 ≠ 0 emitted Coincidences one at a time, H1 D1 one detection all S Coincidences at a P = 0 “in C detection time H2 D the S 2 PC = 0 Singles detection same H2 D 2 P2 ≠ 0 state” (same origin, Singles detection P ≠ 0 direction distribution, 2 energy) Not realized before 1985 D1 et D2 observe random pulses, with a constant mean rate, but no coincidence (PC = 0): anticorrélation • Particle considered “obvious” for electrons, , atoms, molecules: only wave-like effects searched P = 0 : a single particle passes either through H , or through H , not C 1 2 • Case of faint light: particle like behaviour considered “obvious” through both paths simultaneously. A single particle cannot be split. when the average distance between photons is large : only wave- Opposite behavior predicted for a wave: PC ≠ 0 9 like effects searched with very attenuated light 10

The particle-like character of faint light is According to modern quantum faint not proved by photoelectric effect light is not made of single particles Photoelectric effect fully interpretable by the semi-classical model Attenuated light described as a of photo- (Lamb and Scully, 1964) Glauber quasi-classical state, which E • Quantized detector with a ground state and has the same behavior as a classical a continuum of excited states (, , electromagnetic wave. metal …) ET If one insists for speaking of • Light : classical electromagnetic particles: in any interval of time, or E0 cosωt • Fermi golden rule: rate of photo ionization 0 space volume, probabilistic proportional to density of final states distribution of particles P(1) small but P(2) ~ P(1)2 Remark: in 1905 (eight years before Bohr’s atom) no quantum Probability to have two particles never zero. No anticorrelation model, neither for light nor for matter: photoelectric effect expected between two detectors : PC ≠ 0 impossible to understand in classical physics. Einstein chose to quantize light. He could have chosen to quantize matter. Are there means to produce single photon states of light? 11 Can we demonstrate experimentally single particle behavior? 12

2 A beam-splitter to discriminate between a Wave-like behaviour at a particle-like and a wave-like behaviour (AA, Philippe Grangier, 1985) (AA, Philippe Grangier, 1985)

Wave split in Single detection P1 ≠ 0 two at BS: Single detection P1 ≠ 0 Joint one expects single photon detection PC Joint joint detection single photon detection PC ? Pc ≠ 0 wave packet? Single detection P2 ≠ 0

Single detection P2 ≠ 0

More precisely, joint photodetection 2 2 probability proportional to mean square but I ≥(I ) 22 of wave PRTIc = η Single particle: one expects Pc = 0 P for a α =≥C 1 wave while PRIPTI12==ηη , PP12

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A quantitative criterion to discriminate Faint light does not pass single particle test wave-like vs. particle-like behaviour (AA, Philippe Grangier, 1985) Light pulses emitted Particle: one Single detection P ≠ 0 Single detection P ≠ 0 1 by a LED and 1 expects Joint strongly attenuated: Joint Pc = 0 single photon detection PC 0,01 photon per detection PC pulse, on average Wave: one wave packet? expects Single detection P2 ≠ 0 attenuator Single detection P2 ≠ 0 Pc > P1 P2

Experimental result: αmeas = 1.07 ± 0.08 not single particle behaviour P In agreement with classical description of wave splitting. Criterion for a particle like behaviour: α =

Single photon sources Isolating single photons emitters in time (AA, Philippe Grangier, 1985) allows us to design sources of single photons ( n = 1 ) for which a particle like behaviour is expected: J = 0 Assembly of atoms 7 −1 P 551 nm emitting 10 s pairs of e 1 dye laser Isolated ν1 photons. In the 5 ns time excited τ = 5 ns window following P r atom C Kr ion laser detection of ν1, only one ν2 423 nm atom is likely to emit a Emits one n =1 photon ν2 (cf J Clauser, f P Pc = 0 and only 2 J = 0 1974) . one photon ⇒<α 1 In classical light sources (thermal radiation, lamp) many Experimental result: atoms simultaneously excited: (laser also) αmeas = 0.18 ± 0.06 To obtain single photons effects, isolate a single atom emission: • in space (Kimble, Dagenais, Mandel, antibunching) Clear anticorrelation (α < 1) • in time (J Clauser 1974, non classical effects in radiative cascade; Particle-like behaviour AA, PG, heralded single photon, α < 1 ) 17 18

3 Modern sources: single photons emitters Single photon interference? isolated in space and time Isolated 4-level emitter + pulsed excitation (Lounis & Moerner, 2000) Can we observe interference with single photon wave packets (α < 1)?

échantillon 1.0 P “scanner” 0.8 2 piezo. x,y,z Courtesy of J-F Roch, 0.6 0.4 Objectif de ENS M BS 0.2 1 out x 100, ON=1.4 Cachan 0.0 P1 Intensité normalisée 400 500 600 700 Laser Miroir Pulsed exciting laser Longueur d'onde (nm) dichroïque d’excitation single photon V. Jacques et al., EPJD 35, 561 (2005) wave packets M2 APD Si BSin Experimental result Filtre diaphragme Module comptage réjectif 50 μm de photon αmeas = 0.132 ± 0.001 For a review: B. Lounis and M. Orrit, Rep. Prog. Phys. 68, 1129 (2005). Clear anticorrelation (α < 1) Do probabilities P1 and P2 vary (sinusoidally) when one varies the P. Grangier and I. Abram, path difference? Phys. World, Feb. 2003 Particle-like behaviour 19 20

Single photon interference Single photon interference Interferometer with single photon source at input Interferometer with single photon source at input

Mach Zehnder N1 Orsay 1985 N1 interferometer N Mach Zehnder N 2 Vary path difference and stay 2 Vary path difference and stay N N N N 1 2 0.1 second at each position 1 2 1 second at each position

Not much to see!

N1 N2 Clear modulation!

Grangier, AA, 1985 Grangier, AA, 1985 21 22

Single photon interference Single photon interference Interferometer with single photon source at input Interferometer with single photon source at input

Vary path difference and stay Vary path difference and stay Orsay 1985 N Orsay 1985 N 1 10 seconds at each position 1 10 seconds at each position Mach Zehnder Mach Zehnder N2 N2 Experiment done in the single photon N1 N2 N1 N2 regime: P α =

PC N1 N2 N1 N2

P2

N1 N2 Sinusoidal variation! N1 N2 Sinusoidal variation! Remarkable signal to noise Remarkable signal to noise ratio, visibility close to 1. ratio, visibility close to 1.

Unambiguous wave like behaviour 23 Unambiguous wave like behaviour in the single photon regime 24

4 Single photon interference Wave particle duality for single particles

échantillon First experiment P1 ≠ 0 “scanner” A more modern piezo. x,y, Particle like Objectif de Cachan 2005 implementation microscope behaviour: goes either x 100, ON=1.4 Fresnel biprism PC = 0 (Cachan, 2005) Miroir La to one side, or the dichroïque d’exc D1 other, not both. CCD P2 ≠ 0

Filtre diaphra camera réjectif 50 μ D2 Second experiment M BS ObservationAnticorrelation in the on overlapdetectors D1 Wave like behaviour: 1 out betweenand D2: twoαmeas beams:= 0.132 ± 0.001 goes through both interferenceEvidence of fringes?single photon paths (output depends on paths difference) behaviour M2 BSin Same single photon wave packets, same beamsplitter,

Unambiguous wave like behaviour in the single photon regime 25 contradictory images 26

To comfort oneself: Bohr’s complementarity Wheeler’s delayed choice experiment

D2 The two experiments are P1 The two experiments are Which way ? P1 incompatible. One must M1 incompatible. One must D choose the question: 1 choose the question: P = 0 P = 0 • Which way ? C • Which way ? C M • Interference ? • Interference ? 2 P2 P2 The two questions cannot be asked Slightly modify the Interference ? simultaneously “which way” experiment M1 BSout M1 BS out Could it be that the One can choose the photon behaves question by introducing M BS 2 M2 according to the question? in or removing BSout BS in

What would happen if the question was chosen after passage at the One can make the choice after the photon passed BS input beamsplitter? Wheeler’s delayed choice experiment. in 27 28

Wheeler’s proposal (1978) Experimental realization (ENS Cachan)

Electro Optical Modulator: • no voltage = BSoutput removed The choice of introducing or removing the second beamsplitter •V = BS recombines the beams must be space like separated from the passage at first beamsplitter, π output so when the photon passes the first beam splitter it cannot know The choice is made by a quantum random noise generator, after the which measurement will be done. 29 photon passes the first beam splitter. 30

5 Delayed choice experiment: results Delayed choice experiment: results

D Interference ? différence de marche Which way ? 2 M1 M1 BS out BSoutput “removed” D1 BSoutput “inserted” M2

M2 BS in

No interference fringes “Which way” parameter = 99% correlation between detection rate Fringe visibility: Alpha parameter = 0.12 at either detector and blocking of 94 % one path or the other

Path difference The photon travels one route or the other… and we Wave-like behaviour ⇒ both routes 31 can tell which one. 32

Delayed choice experiment: conclusion Wave particle duality: one of the “great mysteries” of quantum mechanics The photon travels Experimental facts us to accept it. Impossible to reconcile one way or both with images coming from our macroscopic world. To comfort routes according to ourselves: the setting when it • Quantum optics formalism gives a coherent account of it arrives at the (one has not to choose one image or the other). position of the • Bohr’s complementarity allows one to avoid too strong output inconsistencies but... beamsplitter. • The delayed choice experiment shows that complementarity should not be interpreted in a too naïve way. The choice, made by a quantum random noise generator, is separated by a space-like interfal from passage at the first beam splitter. Questioning the foundations of quantum mechanics is not only an academic issue. It has led to the development of quantum “Thus one decides the photon shall have come by one route or by information, i.e. and . both routes after it has already done its travel” J. A. Wheeler 33 34

Quantum cryptography with Quantum cryptography with single photons (BB84) single photons (BB84) Eve

Quantum Key Distribution: produce two identical copies of a random sequence of 0 and 1, without an eaves dropper (Eve!) being able to obtain a copy of the key unnoticed • perfect security mathematically proven (R. Shannon) • quantum laws allows one to be sure that there is no http://www.iota.u-psud.fr/~grangier/Photon/QKD-ph-uniques.html eavesdropper looking at a single photon without leaving a trace. 35 36

6 Cryptographie quantique: Delayed choice experiment: the team Schéma BB84 avec photon unique Frederic François E Groshans Treussart Wu Jean-François Groupe d’Optique Vincent Roch Quantique de Jacques l’Institut d’Optique (P. Grangier) and the god fathers of that experiment

Laboratoire de photonique ENS Cachan (J F Roch)

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Delayed choice experiment: one of the two big Delayed choice experiment: one of the two big quantum mysteries (Feynman, 1960, 1982) quantum mysteries (Feynman, 1960, 1982) Single particle interference experiment (1 particle)

EPR correlation (2 entangled particles) EPR correlation (2 entangled particles) • No local realistic description (violation of Bell’s inequalities) • Bohm’s hidden variables description is non-local Wheeler’s delayed choice experiment (1 particle) • Local realistic description possible (Bohm’s hidden variables) Wave-particle duality (one particle) is not as big a mystery as entanglement (elementary many-body problem) 39 40

Delayed choice experiment: one of the two big quantum mysteries (Feynman, 1960, 1982)

Wheeler’s delayed choice experiment (1 particle) EPR correlation (2 entangled particles) Are they “only” academic (epistemological) questions? Studies of these questions have led to the development of : quantum computing (based on entanglement) and quantum cryptography (based on single photons or entanglement) 41

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