Squeezed States — Quantum Harmonic Oscillator

Wigner quasi-probability distribution · Heisenberg uncertainty · quadrature squeezing

State Parameters

Δx·Δp = 0.500 ħ/2

Quadrature variances

Key insight: Squeezed states satisfy Heisenberg equality Δx·Δp = ħ/2, but redistribute the uncertainty — one quadrature below shot noise (1/2) while the other grows.

Wigner function: W(x,p) can be negative (non-classical!) for Fock states n≥1 and certain superpositions. Negativity is a witness of quantum weirdness.

Squeezing factor: Δx = e⁻ʳ/√2, Δp = eʳ/√2