Spin Squeezing 2D: Exact One-Axis-Twisting in the Dicke Basis

The paired 3D simulator visualizes one-axis-twisting spin squeezing using the standard linearized (Holstein–Primakoff) shortcut: a round quantum-noise disk sheared into an ellipse by a fixed-length approximation. This 2D companion computes the same physical setup — N atoms, collective spin, H = χJz² — a completely different way: by directly evolving the exact (N+1)-dimensional quantum state in the permutation-symmetric Dicke basis and computing every readout from real ladder-operator matrix elements, with no linear approximation anywhere. The result recovers the linear model exactly in the large-N limit (shown live in the comparison strip) while also exposing two effects the linear shortcut cannot see: the collective spin's own length contracts as it squeezes, and for small ensembles pushed past their optimal shear the noise ellipse curves back around and re-grows instead of shrinking forever. Sweep the shear, atom number and readout angle to watch an exact quantum calculation and a mean-field approximation agree, then visibly part ways.