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 Incoming links: Ion trap

Norman Foster Ramsey, Jr. received one half for inventing the separated oscillatory fields method and applying it to the hydrogen maser and other atomic clocks. Hans G. Dehmelt and Wolfgang Paul received one quarter each for developing ion trap techniques.^[ref]

Use the common

D_{3/2}

level to subtract the two upper-state energies. The indicated transition satisfies

\frac{1}{λ} = \frac{1}{397 nm} + \frac{1}{850 nm} - \frac{1}{866 nm}, λ ≃ 393.6 nm .

The 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} ℏ ω_{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]

Without interaction, the two-qubit Hamiltonian operator is

H_{a} \otimes I + I \otimes H_{b}

, so its evolution factors as

U_{a} \otimes U_{b}

. It maps each product state to another product state, and cannot implement an entangling two-qubit gate such as a CNOT gate.

In an ion trap, the Coulomb interaction couples the ions' displacements into collective vibrational normal modes. The qubit states are internal atomic states; lasers coupling internal excitation to creation or annihilation of a shared vibrational quantum allow that motion to carry conditional information between ions. Thus the physical mediator is a collective motional normal mode of the Coulomb-coupled chain, rather than a direct resonant exchange between isolated internal qubit transitions. Ground-state cooling and resolved motional sidebands support the ideal pulse model used here.

The five DiVincenzo criteria are: a scalable collection of well-characterized qubits; preparation in a known fiducial quantum state; relevant coherence times long compared with quantum gate times; a universal quantum gate set; and qubit-specific quantum measurement. The criterion is useful control of the whole computation, including errors, rather than merely observing two resolved levels.^[ref]

For trapped ions, the implementation is:

Scalable characterized qubits. Two long-lived hyperfine structure levels or an optical ground/metastable pair in each ion encode $∣0 ⟩, ∣1 ⟩$ . An ion trap confines individually addressed ions. Extending a chain adds qubits, but increasing motional complexity, addressing errors and heating limit straightforward scaling; segmented traps and transport can help.
Initialization. Optical pumping prepares the internal quantum state. Doppler cooling and, where required, resolved sideband cooling prepare the shared motion used for quantum gates.
Coherence. Long-lived internal levels give coherence much longer than controlled pulse times. Magnetic noise, laser noise, scattering and motional heating cause quantum decoherence; suitable clock-state encodings and control reduce these errors.
Universal control. Resonant optical, microwave or Raman transitions give arbitrary one-qubit rotations. Shared motional normal modes, coupled through the Coulomb force, mediate entangling two-qubit gates. Together these supply a universal quantum gate set.
Readout. State-selective cycling fluorescence, often with electron shelving, produces a bright/dark signal resolved for individual ions.

For trapped neutral atoms, the corresponding implementation is:

Scalable characterized qubits. Long-lived ground-state hyperfine structure levels encode qubits in an optical lattice or an array of optical tweezers. Large arrays are feasible, but random loading, vacancies, atom loss and individual addressing must be controlled.
Initialization. Cooling plus optical pumping prepares the internal quantum state. Filling or rearranging traps prepares a usable register; motional cooling is needed when the chosen quantum gate depends on motion.
Coherence. Weak environmental coupling of neutral ground-state chemical atoms allows long coherence. Trap-light scattering, differential light shifts and magnetic noise limit it; switching traps or choosing suitable encodings can reduce these effects.
Universal control. Microwave or Raman transitions implement one-qubit rotations. Ground-state chemical atoms do not have the ions' long-range Coulomb force, so that motional-bus construction cannot simply be copied. Controlled collisions or Rydberg blockade can nevertheless supply entangling two-qubit gates.
Readout. State-dependent fluorescence or state-selective removal followed by imaging identifies a chosen qubit. Optical resolution, cross-talk and atom loss constrain repeated measurements.

Thus neither platform is forbidden from meeting a criterion in principle. Weak neutral-ground-state interactions make entangling control harder, but claiming that trapped neutral atoms cannot implement a universal quantum gate set would be false. Gate-model quantum algorithms using Rydberg blockade had already been demonstrated in a programmable neutral-atom processor by 2022.^[ref]