Linear Paul Trap: Ion Coulomb Crystal

Trapped-ion quantum computers — the platform behind IonQ and Quantinuum's roadmap to error-corrected machines — hold their qubits in a linear Paul trap: an oscillating RF quadrupole field confines ions radially while static endcap electrodes confine them along the trap axis. This simulator integrates the real Mathieu equation of motion for each ion under the time-dependent RF drive plus full pairwise Coulomb repulsion, so the ions self-assemble into a linear crystal exactly as they do in a real trap. Tune the RF amplitude and DC endcap voltage to explore the Mathieu stability diagram, dial in laser-cooling damping to watch a hot ion cloud settle into a still crystal, and change the chain length — all while live readouts track the stability region, secular frequency, crystal spacing and kinetic energy.