Parametric Amplification & Squeezed Light

OPA · Wigner function · Heisenberg uncertainty ellipse · ΔX₁·ΔX₂ ≥ 1/4

OPA Parameters

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.