Spin Squeezing: One-Axis Twisting Below the Standard Quantum Limit

Every unentangled sensor — a classical light beam, an ensemble of independent atoms — is bounded by the standard quantum limit: its noise floor falls only as 1/√N with the number of probes. Spin squeezing beats that bound by entangling the probes with each other. This simulator visualizes one-axis twisting, the mechanism used in cold-atom clocks and quantum magnetometers: a collective atomic spin's round quantum-noise disk is sheared by a Jz² interaction into an ellipse of the same area, compressing the noise along one axis below shot noise while it grows along the perpendicular one. Drag the atom-number and shear controls (or let the auto-sweep animate the twist), then sweep the readout-axis slider to find the angle where the live squeezing parameter ξ², its decibel sensitivity gain, and the projected variance all show a real quantum advantage over the SQL.