Trapped-Ion Qubits Simulator

Linear Paul Trap

Ion chain length 5

Confinement strength 1.0

Ion spacing

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Chain length

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Phonon energy

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RF phase

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How it works

Four RF rod electrodes surround the trap axis; adjacent rods carry opposite-sign oscillating voltage, so the instantaneous field always pushes an ion inward on average — a time-averaged pseudopotential that confines ions radially even though no static field alone could. Static end-cap electrodes add a harmonic potential along the axis. Each ion sits where its axial confinement force balances Coulomb repulsion from its neighbours, so the chain self-organizes into an evenly-spaced Coulomb crystal — the same mechanism used in real Ca⁺ / Yb⁺ ion-trap quantum computers.

F_axial(i) = -k·z_i
F_coulomb(i) = Σ_j q²/(z_i-z_j)²·sign(z_i-z_j)
equilibrium: F_axial(i) + F_coulomb(i) = 0

Ion chain length — more ions add more mutual Coulomb repulsion, stretching the crystal.
Confinement strength — a stiffer axial trap pulls ions toward the centre, compressing the spacing against Coulomb repulsion.
Excite phonon mode — kicks every ion in phase along the axis, exciting the collective centre-of-mass vibrational mode (a phonon). In real trapped-ion computers, a laser tuned to this shared vibration lets two distant ions swap quantum information through it — the mechanism behind the Mølmer–Sørensen entangling gate.

Real-world relevance: trapped-ion qubits are one of the leading quantum-computing platforms (IonQ, Quantinuum) precisely because this phonon bus lets any two ions in the chain couple to each other, not just nearest neighbours.

Ion (Ca⁺/Yb⁺) RF rod (+ phase) RF rod (− phase) Coupling laser

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