Quantum op*cs Chris Westbrook Antoine Browaeys
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
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
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
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
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 +1 +1 2 +1-1 Concept of entanglement
The early days (1900-1940) 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
«Modern» quantum op*cs (1956 1990) 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 )
Expansion towards applica*ons (1990?) 1995 - Beginning of quantum informa;on & entanglement 2000 - New single photon sources based on single emilers 2001 - Analogy between Bose-Einstein condensa;on and quantum op;cs 2005 - Hanbury-Brown &Twiss, HOM, with atoms: towards «atomic quantum op;cs»? (Ins;tut d Op;que) 2010 - Quantum op;cs with microwaves photons, ions, quantum circuits!! 2012-2 photons can interact in special media: NL Op;cs with individual photons!!!
Cosmic microwave background radia*on Penzas and Wilson 1964 «Cobe» mission: Nobel 2006
Black Body radia*on: fluctua*ons (anisotropies) ΔT / T ~ 10-4 Measured by the Planck mission (2013-2014)
11 1 1 111111111 1111111 111111 111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 11111
1 16 OQ 1 Bbody.nb [ [ //// // / /_] ] 1111111 ω 111111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
16 OQ 1 Bbody.nb 1 11111111 11111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1(ω) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1111111111ρ(ω)1111 (ω) = ρ(ω)11111-11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 111111111111 (ω) = (ω)111111 π - 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11111111111111111ρ(ω) Σ 1 π ω ω ω ρ(ω) = ω π (ω) = π ω 1111111111111 11111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11111111111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (ω) ω 1 1 1 1 11111111111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 111111 = - -ħω / -ħω / 11111 = = ħω / - 111 -ħω / = - (ħω/ ) -ħω / 11111111 ħ ω 1 1 1 1 1 1 1 1 1 1 1 1 1 1 111 (ω) = ħω π ħω / -
1 16 OQ 1 Bbody.nb 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1111111 1 111 111 111111111111 111111111111 11111111111111 11111111111111 111 1 1111111111 111 1 11111111 ħ ω 1 111111111111111 1 (ω)11111111 111 1 111 (ω ) 111 1 11 (ω ) 111 1 11 1111111111111 1 111111111111111 111111111 11111111 11111111 1 11 111111111 111 π = / 1111111 1 111111 π = - (ω ) π + (ω ) π + π π = -π 1111111111111111 111111111111111 1111111111 π = π = 11111111111 π 11 111 = -ħω / 11111111 π (ω ) = ħ ω / - 1111111(ω ) 11 1111 = 1 111(ω)1111111111111 11ω 11111111111ω 11 11111 111111111 ħω (ω) =1 ħω π ħω/ = ħω - π (ω) 1(ω)1111111111111111 111111111111 111 11111111 111111 π 1
16 OQ 1 Bbody.nb 1 1 11111111111111 1111111111111 11111 11111111 1111 1 1 111 1 111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 111111111111 111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1111111 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11111111111111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1111111111111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11111 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 = (ω ) π = (ω ) (ω ) π 1(ω) = ħω / 1111111 111111-1 1 1 1 1 1 1 1 1 1 1 1 1 1ω 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1(ω) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1(ω - ) 1 1 1 1 1 1 1 1 1ω 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1ω 1 1 1 1 1 1 1 1 1 1 1 (ω) 1 1 1 1 1 1 1 1 > 1 1 1 1 111 < 111 1 1 ω 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1(ω) 1 1 1 1 1 1 1 1 1 1 1 1 1 11111111ω1111111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 16 OQ 1 Bbody.nb ([ω] - ) - {ω } 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1111111111111111111 111111111 111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ω = ω + 11111111111 + = π (ω + ) π (ω ) + d dω 1 1+ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 / ω 1 1 1 1 1 1 1 1ħ ω 1 1 1 1 1 1 1 1 1 1 1 ħ ω 1111111111 = ħ 1 1 1 1 1 1 1 1 1 1 1 - = π (ω - ) π (ω ) - d dω 1 1 1 1 1 1 1-ħ 1 1 1 1 1 + + - = π (ω ) 1 111 1111111 + = π (ω + ) π (ω ) + d dω - = π (ω - ) π (ω ) - d dω 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d d = ħ ( + - + - - + - )
16 OQ 1 Bbody.nb 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 111111111 ħ d dω (π - π ) = α 1 111111111111111111 1 1 1 1 1α 1 1 1 1 1 1 1 1 1 1 d dω 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 111 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11111111111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 111111111111 11111τ11 111 1111 + τ + Δ = 1Δ11111111111 11 1 1 1 1Δ 1 1 Δ = 1 1 1 1 1 1 1 1 1 11 ( + τ + Δ) = + τ + Δ + τ + Δ + Δ τ = 1 1 1 1 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1Δ 1 1 1 1 1 1 1 1 1111111τ11 1111111τ11 111 Δ τ = - = - α 11 111111111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1Δ 1 1Δ 1 1 1 1 1 1 1 1ħ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1ħ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1τ 1 1 1 1 11 Δ τ = (ħ ) ( + + + + - + - ) = (ħ ) (ω ) (π + π ) = (ħ ) (ω ) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11111111111111 1111111111ħ 1111 1 1 1 1 1 1 1(ħ ) π 1 1 1 1 1 1 1 1 111
1 16 OQ 1 Bbody.nb Δ τ = (ħ ) (ω ) + δ π 1 1 1 1 1 1 1 1 1 1 1 1δ ħ 1 1 1 1 1111δ = 1 1 1 1 1 1 1 1 1 1 1 1 1 111111 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 π π = -ħω / 11111 = π π-π + δ π π -π π π 1δ = 111 = 111111111 π 1 1π = / 1 1 1 1 1 1 1 1 1 1 1δ = 1 1 1 = 1111111 11111 111 11111 1 1111 11111 111 1111 1111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 111111( )111111 + + = = ħω 1 1 1 1 1 1 1 1ħω 1 1 1 1 1 1 1 1 1ω 1 111111111111111ħω11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1111111ħω11ħω + dħω1 = = π d = π ħ ω dω 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1111 111111111
16 OQ 1 Bbody.nb 1 ω ω = π ω 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1111111111111 1 111 111111111 11 111111111111111-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 = = 1 1 1 1 1 1 1 1 1 1 1( + - )! 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11111( - )!11111111111 1 1 1 1 1 1 1 1 1 1 1 1 1 1! 1 1 1 1 1 1 1 1 1ħ ω 1 1 1 1 1 1 1 111 = ω (ω+ω-)! ω! (ω-)! 1 1 ω 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 = ω ω ħω11 1 1 1 1 1 1 ω 1 1 1 1 1 1 1 1 1 1 11 11 ( 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 + 1 1 1 1 1 1 1 1 1 1 1 ω 1 1β 1 1 1 1 1 1 1 1 1 1 ω + ω - ω + ω 1 1 1 1 1 1 1 11 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 = - 111111 ω 111111111111 11111dω1111111 11β 1( ) - 1 1 1 1 1 1 1 1 1 1 1 1ħω 1 1 11