1 Etats quantiques Fermions et bosons (ex. de cours) 2 Paradoxe

◦6
ϕ1(~x)|S1i
|ψ1i=|ϕ1i⊗|S1i ∈ L2R3⊗C2|ψ2i=|ϕ2i⊗|S2i
|ψ1i |ψ2i
|ψ1i∧|ψ2i=1
√2(|ψ1i⊗|ψ2i−|ψ2i⊗|ψ1i)
|S1i=|S2i=|Si
ϕ(~x1, ~x2)ϕ1(~x1)ϕ2(~x2)
ϕ1=ϕ2=ϕ
z
|xi,|yi
x, y
y
x
Polarisation
|x> Polarisation
|y>
z
Photon, vitesse
c=300 000 km/s
|Pi
|θi
θ x (x, y)
θ
x
z
| >θ
y
x
|xi
|yi|Pi
|θi
Photon
Polar.
z
|y> Absorbé
Filtre // x Filtre // x
Photon Passe
Polar. |x>
z
x
y
x
y
|θiθ
I0θ
I1
x Ax= 1 Ax=−1hAi
hAi= (+1) ×+ (−1) ×
ˆ
Aˆ A|xi= (+1) |xiˆ A|yi= (−1) |yi
|Pi hAi |Piˆ A

1 2
|P12i=1
√2(|x1i|y2i−|y1i|x2i)
z
x
y
Photon 2Photon 1 Atome
x
y
y’
x’θ
θ
|P12i |x0i,|y0i(x0, y0)
θ(x, y)
u, v θu, θvx
AuAu=±1
BvhAuBvi=−cos (2 (θv−θu))
θu→0θv→θ=θv−θu
ˆ
B≡ˆ R(θ)ˆ Aˆ R(−θ)
z
θ
u
u
v
θ
v
Filtre 1 //u
12
|P >
x
y
Filtre 2 //v
u, v, w φ/2
∆ (φ) = hAuBvi−hAuBwi+hAvBvi+hAvBwi
u
v
w
φ/2
φ/2
∆quantique (φ) = cos 2φ−2 cos φ−1
i
j
O
0
∆(φ)
2
−2 ∆quantique φ
π
O
hOi=ROdµ µ
A=AuA0=AvB=BvB0=Bw
∆loc (A, A0;B, B0) = hABi−hAB0i+hA0Bi+hA0B0i
|A|,|A0|,|B|,|B0|= 1 |∆loc| ≤ 2|∆loc| ≤
|hABi−hAB0i| +|hA0Bi+hA0B0i|
|P12i |∆quantique (φ)| ≤ 2√2