One-axis twisting H=χJ_z² squeezing noise below the standard quantum limit
One-axis twisting H=χJ_z² generates spin-squeezing by creating quantum correlations between N two-level atoms. The Bloch sphere coherent state (CSS) has equal quantum noise ΔJ_y=ΔJ_z=√N/2. Squeezing reduces noise in one component below the SQL (ξ²=N(ΔJ_perp)²/|⟨J⟩|²<1) at the cost of increased conjugate noise. Used in atomic clocks to beat the standard quantum limit; achieved in BECs and optical lattice clocks.