Parametric Amplification & Squeezed Light
OPA · Wigner function · Heisenberg uncertainty ellipse · ΔX₁·ΔX₂ ≥ 1/4
OPA Parameters
Squeezing parameter r:
1.20
Squeezing angle θ (rad):
0.00
Displacement α (coherent):
1.50
Show:
Vacuum
Ellipse
ΔX₁ (squeezed):
—
ΔX₂ (anti-sq):
—
ΔX₁·ΔX₂:
—
Squeezing dB:
—
Squeezed vacuum:
S(r,θ) = exp[½r(e^{-2iθ}a²−h.c.)]
Wigner function is a Gaussian with squeezed quadratures:
ΔX₁ = ½e^{-r}, ΔX₂ = ½e^{r}
Minimum uncertainty state: ΔX₁·ΔX₂ = ¼ always.
Squeezing dB = −20r·log₁₀(e) ≈ −8.686r dB.
Used in gravitational wave detection (LIGO), quantum communication, quantum metrology.