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Ignacio Cirac and Peter Zoller showed how laser control of a chain of trapped ions could implement quantum computation. Their proposal transfers information between an ion's internal quantum state and a collective vibrational normal mode, then uses that shared motion to perform a conditional operation on another ion. Returning the motion to its starting quantum state leaves the intended quantum logic gate acting on the internal qubits.^[ref]

Use the common $D_{3/2}$ level to subtract the two upper-state energies. The indicated transition satisfiesThe value inherits the rounding of the supplied wavelengths. It is shorter than 397 nm because $P_{3/2}$ lies above $P_{1/2}$.

A static electric potential alone cannot confine a charge stably in all three dimensions in a charge-free region. An RF quadrupole ion trap uses a rapidly alternating electric field to provide effective radial confinement; DC endcap fields can supply axial confinement. Near a stable equilibrium, the secular motion sees an approximately harmonic pseudopotential. It has quantized vibrational levels $E={\sum }_i\hslash {\omega }_i(n_i+1/2)$, with separate normal modes along the principal directions. RF Paul trap micromotion is superposed on this slower secular oscillation. For several trapped ions, Coulomb interactions instead give collective normal modes. ^[ref]