Mølmer–Sørensen Gate — Phase-Space Diagram

This is a native 2D counterpart of the Mølmer–Sørensen trapped-ion gate simulator. Rather than rendering a 3D ion trap, it plots the shared motional mode's coherent amplitude directly in the complex phase plane: a bichromatic laser drive traces a closing circular loop, and the area swept out by that loop — accumulated live with a shoelace-formula integral — is exactly twice the geometric two-qubit entangling phase. A companion population disk shows the resulting |gg⟩/|ee⟩ superposition rotating as the phase builds, reaching the maximally entangled Bell state exactly when the loop closes with Θ = π/4. Adjust the drive strength Ω_eff and detuning δ, choose how many loops the gate completes, and watch the phonon number return to zero exactly when the loop closes — the signature that makes this gate robust against motional heating.