The Squeezed State — Sub-Poissonian Light and Quantum-Enhanced Sensing
Act 19 of the NexusOS physics sequence. First disclosed 2026-07-21. AGPL-3.0. Founder: Te Rata Pou.
Definition
A squeezed state compresses noise in one quadrature below the vacuum level while inflating the conjugate quadrature to preserve ΔxΔp=ℏ/2. Single-mode squeezing operator: S(ξ)=exp(ξ★â²/2 − ξ↲/2), where ξ=r·e^(iθ) and r is the squeezing parameter.
Quadrature Noise
For squeeze angle θ=0: Δx=e^(−r)·√(ℏ/2mω) (squeezed), Δp=e^r·√(ℏ/2mω) (anti-squeezed). At r=1.15 (10 dB squeezing): Δx reduced to 31.6% of vacuum. Record squeezing: −15 dB (Vahlbruch 2016).
Sub-Poissonian Statistics
The Mandel Q-parameter < 0 for squeezed vacuum and amplitude-squeezed states. Photon statistics deviate from Poisson — this is a non-classical signature observable with photon-number-resolving detectors.
Two-Mode Squeezing and EPR Entanglement
Two-mode squeezing S₂(ξ)=exp(ξ★â_sâ_i − ξâ†_sâ†_i) produces signal-idler entanglement. In the limit r→∞: x_s+x_i→0 and p_s−p_i→0, reproducing the original EPR state.
WNSP Connection
Squeezed light at λ=1550 nm reduces phase noise below the shot-noise limit in SNIC WGM cavities. A 10 dB squeezed input reduces phase estimation uncertainty by √10 — equivalent to averaging 10× more photons without extra power. Critical for long-distance Ψ channel fidelity.
The 20-Act Sequence