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Incoming links: P. Zoller
A Paul trap uses a time-dependent electric quadrupole field to provide dynamic confinement, avoiding the impossibility of trapping a charge in a stable three-dimensional static electrostatic minimum. Its dynamics follows a Mathieu equation: stable drive parameters produce slow Paul trap secular motion with superposed fast Paul trap micromotion. If denotes the peak oscillating field, the effective energy for small Paul trap micromotion isThe radiofrequency pseudopotential of a Paul trap is an averaged mechanical energy, not a static electrostatic potential. Doppler cooling and, where needed, resolved sideband cooling reduce Paul trap secular motion; the Lamb-Dicke regime suppresses higher motional sidebands.[ref]
Nobel Lecture: Superposition, entanglement, and raising Schrödinger’s cat by David J. Wineland. Sections III–IV, confinement, internal-state control and quantized ion motion
Two long-lived internal states encode a qubit, for example hyperfine states, while an optical metastable transition provides another option. Optical pumping initializes it. Resonant or Raman transition pulses make coherent single-qubit rotations, and state-dependent fluorescence distinguishes a bright state from a dark shelved state. Shared quantized normal modes let one ion's internal state influence another, providing entangling gates in the proposal of J. I. Cirac and P. Zoller; the motional bus must be returned to its intended state rather than left carrying unwanted information.[ref]
Quantum Computations with Cold Trapped Ions by J. I. Cirac and P. Zoller. 1995, pp. 4091–4093, shared motion and conditional gates
A concrete early experiment demonstrated a controlled-NOT gate between the internal hyperfine and motional degrees of freedom of a single trapped ion. This was an internal–motion two-qubit gate, not yet a gate between two separate ions.[ref]
Demonstration of a Fundamental Quantum Logic Gate by Christopher Monroe and others. 1995, pp. 4714–4717, encoding and gate demonstration
Challenges include electric-field-noise heating of the motional bus, excess Paul trap micromotion from stray fields, magnetic and laser phase noise, off-resonant spontaneous scattering, imperfect preparation and readout, and unwanted excitation of spectator modes. Scaling to many ions adds mode crowding, individual-addressing crosstalk and transport requirements. Cooling and quantum error correction must remove entropy without erasing stored qubits. Long storage coherence is necessary but not sufficient: gates and measurements must also be accurate and reproducible. The original gate experiment explicitly identified laser, field, trap-drive and motional decoherence limitations.[ref]
Demonstration of a Fundamental Quantum Logic Gate by Christopher Monroe and others. p. 4716, decoherence sources and limits to extended computations