It is not possible to produce a three-dimensional potential well to trap charged particles using electrostatic forces alone. Ion traps therefore use either a combination of electric and magnetic fields (the Penning trap) or time-varying electric fields (the rf or Paul trap). Trapped ion optical frequency standards are studied under low magnetic field conditions using the Paul trap or one of its variants.
These schemes are based on the use of cylindrically symmetric quadrupole electric potentials of the form
φ(r, z, t) = A(t) (r2 - 2z2).
An ideal Paul trap uses three electrodes, a ring and two endcaps, which are hyperbolic in shape and whose surfaces represent equipotentials of the quadrupole potential. The function A(t) is the potential applied between the ring and endcaps, and has both oscillating and static parts. If the trap parameters are chosen correctly, this gives stable confinement in all directions in an effective time-averaged potential known as a pseudopotential.
Although hyperbolic electrodes give the best approximation to a quadrupole potential over a large volume, optical access to such a trap is very poor. In general a much simpler electrode structure is sufficient to approximate the harmonic potential for an ion which is laser-cooled to low temperatures and hence confined close to the centre of the trap. Such traps are much easier to manufacture and allow improved optical access to the ion.
Endcap traps are used at NPL for optical frequency standards applications. The relatively open structure of this trap improves the optical access to the ion. This means that cooling beams can be oriented to enter the trap from several directions, allowing the ion motion to be controlled and monitored in all three dimensions.
With either a Paul or endcap trap, the coldest ion temperatures can be reached when there is only one ion in the trap. This ion also has to be at the trap centre, where there is no electric field to cause 'micromotion' at the rf drive frequency of typically 15 MHz. The ion motion then comprises only relatively slow motion at typically 1 MHz ('secular' motion). In order to move the ion to the trap centre, dc voltages are applied either to the endcap electrodes or to compensation electrodes around the trap.
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