Spin Squeezing — Quantum Fisher Information

Spin Squeezing Physics: Start with N spin-½ particles all pointing in the x-direction (coherent spin state). One-axis twisting Hamiltonian H = χJz² generates squeezing: one quadrature of noise shrinks below the Standard Quantum Limit (SQL) while the orthogonal one grows. The SQL for phase estimation: δφ_SQL = 1/√N (shot noise). Squeezed states achieve δφ_SQL → 1/N^(2/3) (Heisenberg limit is 1/N). Quantum Fisher Information F_Q = 4·Var(Jθ) quantifies the metrological gain. Wineland squeezing parameter: ξ² = N·min_θ[Var(Jθ)]/(⟨J⊥⟩²) — squeezed when ξ² < 1. Used in atomic clocks (NIST 2010) and gravitational wave detectors.