Parametric Amplification & Squeezing

A harmonic oscillator with k(t) = k₀(1 + ε·cos 2ω₀t). Phase-space trajectories show one quadrature amplified exponentially while the other is squeezed — the uncertainty ellipse rotates and deforms. Near resonance (ε→1), instability grows.

Phase space (q, p)
q(t) — position vs time
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t = 0