Quantum op*cs. Chris Westbrook Antoine Browaeys

Transcription

1 Quantum op*cs Chris Westbrook Antoine Browaeys

2 Important phenomena that CANNOT be explained classically Discovered before 1945 Discovered acer 1945 Spectum of blackbody radia;on Photo-electric effect Spontaneous emission by an atom Loop correc;on : Lamb shic in H atom Non-intui;ve correla;ons in the E&M field Hanbury-Brown and Twiss effect An;-correla;on at a beam spliler Hong-Ou-Mandel effect squeezing : reduc;on of shot noise Viola;on of Bell s inequali;es All well explained by quan*zed E&M field

3 An*-correla*on at a beamsplimer Photons are indivisible. Send a photon on a 50/50 beam spliler. d You can detect a photon in c and d, but never both. This is not what happens in classical E&M. c d On the other hand, you can observe interference at port e and f, even with single photons. Photons can split!! c θ e f

4 Hong-Ou-Mandel effect (1986) How strange are single photons! What happens if you send a single photon into port a and one into port b of a 50/50 beam spliler? b d a You never detect exactly one in c and d at the same ;me!! c

5 Photon shot noise If you detect on average N photons in an experiment (say at port e) the standard devia;on is N (poissonian sta;s;cs as if the photons were independent) d c θ e f No!! With a specially prepared field you can have reduced noise

6 Bell s inequali*es & entanglement Not only are the correla;ons non-intui;ve they are non-local: i.e. correla;ons observed at a and b cannot be explained by a local correla;on, present in the source S +1-1 I a ν 1 S b II ν Concept of entanglement

7 The early days ( ) 1900 Planck s law of black body radia;on 1905 Explana;on of the photo-electric effect by Einstein. Idea of photon 1926 Lewis invents the name «photon» 1927 Quantum theory of radia;on by Dirac and Fermi

8 «Modern» quantum op*cs ( ) 1956 Hanbury-Brown & Twiss experiment Intensity correla;ons 1963 Quantum theory of photo-detec;on and coherence by R. Glauber (Nobel 2005) 1977 Photon an;bunching (Kimble, Mandel) 1981 Test of quantum physics using quantum op;cs (Aspect) 1986 Single-photon source and interferences with single photon (Grangier et Aspect) 1987 Two-photon interferences (Hong, Ou et Mandel) Squeezed states of light (Slusher )

9 Expansion towards applica*ons (1990?) Beginning of quantum informa;on & entanglement New single photon sources based on single emilers Analogy between Bose-Einstein condensa;on and quantum op;cs Hanbury-Brown &Twiss, HOM, with atoms: towards «atomic quantum op;cs»? (Ins;tut d Op;que) Quantum op;cs with microwaves photons, ions, quantum circuits!! photons can interact in special media: NL Op;cs with individual photons!!!

10 Cosmic microwave background radia*on Penzas and Wilson 1964 «Cobe» mission: Nobel 2006

11 Black Body radia*on: fluctua*ons (anisotropies) ΔT / T ~ 10-4 Measured by the Planck mission ( )

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13 1 16 OQ 1 Bbody.nb [ [ //// // / /_] ] ω

14 16 OQ 1 Bbody.nb (ω) ρ(ω)1111 (ω) = ρ(ω) (ω) = (ω) π ρ(ω) Σ 1 π ω ω ω ρ(ω) = ω π (ω) = π ω (ω) ω = - -ħω / -ħω / = = ħω / ħω / = - (ħω/ ) -ħω / ħ ω (ω) = ħω π ħω / -

15 1 16 OQ 1 Bbody.nb ħ ω (ω) (ω ) (ω ) π = / π = - (ω ) π + (ω ) π + π π = -π π = π = π = -ħω / π (ω ) = ħ ω / (ω ) = 1 111(ω) ω ω ħω (ω) =1 ħω π ħω/ = ħω - π (ω) 1(ω) π 1

16 16 OQ 1 Bbody.nb = = (ω ) π = (ω ) (ω ) π 1(ω) = ħω / ω (ω) (ω - ) ω ω (ω) > < ω (ω) ω

17 1 16 OQ 1 Bbody.nb ([ω] - ) - {ω } ω = ω = π (ω + ) π (ω ) + d dω / ω ħ ω ħ ω = ħ = π (ω - ) π (ω ) - d dω ħ = π (ω ) = π (ω + ) π (ω ) + d dω - = π (ω - ) π (ω ) - d dω d d = ħ ( )

18 16 OQ 1 Bbody.nb ħ d dω (π - π ) = α α d dω τ τ + Δ = 1Δ Δ 1 1 Δ = ( + τ + Δ) = + τ + Δ + τ + Δ + Δ τ = = Δ τ τ Δ τ = - = - α Δ 1 1Δ ħ ħ τ Δ τ = (ħ ) ( ) = (ħ ) (ω ) (π + π ) = (ħ ) (ω ) ħ (ħ ) π

19 1 16 OQ 1 Bbody.nb Δ τ = (ħ ) (ω ) + δ π δ ħ δ = Δ τ = - α (ħ ) (ω ) + δ π = - ħ d dω (π - π ) 111d / dω1 d dω ω=ω = - ħ ħω / ħω / - = - ħ π π-π π π-π π π = -ħω / = π π-π + δ π π -π π π 1δ = 111 = π 1 1π = / δ = = ( ) = = ħω ħω ω ħω ħω11ħω + dħω1 = = π d = π ħ ω dω

20 16 OQ 1 Bbody.nb 1 ω ω = π ω = = ( + - )! ( - )! ! ħ ω = ω (ω+ω-)! ω! (ω-)! 1 1 ω = ω ω ħω ω ( ω ) = Σ ω ( ω+ω-)! + β( - Σ ω ħ ω ω ) 1 ω! (ω-)! Σ ω ( ω + ω - ) ( ω + ω - ) - ω ω - β ħ ω ω ω 1 1β ω + ω - ω + ω ω d = Σ ω ( ω + ω ) + - ω - - βħω = dω ω+ω ω 1 1 ω = ω = βħω ω = ω βħω - ω π dω β ħ ω - 1 β ħ ω = ω dω β 1( ) ħω