The uncertainty in the frequency of a linear- ion-trap frequency standard (LITS) can be reduced substantially by use of a very small magnetic inhomogeneity tailored to compensate for the residual second-order Doppler shift. An effect associated with the relativistic time dilatation, one cause of the second-order Doppler shift, is ion motion that is attributable to the trapping radio- frequency (RF)electromagnetic field used to trap ions. The second- order Doppler shift is reduced by using a muli-pole trap; however it is still the largest source of systematic frequency shift in the latest generation of LITSs, which are among the most stable clocks in the world. The present compensation scheme reduces the frequency instability of the affected LITS to about a tenth of its previous value.

A Typical Latest-Generation Multipole LITS contains a quadrupole trap and another multipole (e.g., 12-pole) trap surrounded by a coil that generates a nominally uniform axial magnetic field. In the present compensation scheme, a controlled magnetic inhomogeneity is introduced by use of a compensation coil.
The basic principles of prior generation LITSs were discussed in several prior NASA Tech Briefs articles. Below are recapitulated only those items of basic information necessary to place the present development in context. A LITS includes a microwave local oscillator, the frequency of which is stabilized by comparison with the frequency of the ground state hyperfine transition of 199Hg+ ions. The comparison involves a combination of optical and microwave excitation and interrogation of the ions in a linear ion trap in the presence of a nominally uniform magnetic field.

In the current version of the LITS, there are two connected traps (see figure): (1) a quadrupole trap wherein the optical excitation and measurement take place and (2) a 12-pole trap (denoted the resonance trap), wherein the microwave interrogation takes place. The ions are initially loaded into the quadrupole trap and are thereafter shuttled between the two traps. Shuttling ions into the resonance trap allows sensitive microwave interrogation to take place well away from loading interference. The axial magnetic field for the resonance trap is generated by an electric current in a finely wound wire coil surrounded by magnetic shields.

In the quadrupole and 12-pole traps, the potentials are produced by RF voltages applied to even numbers (4 and 12, respectively) of parallel rods equally spaced around a circle. The polarity of the voltage on each rod is opposite that of the voltage on the adjacent rod. As a result, the amplitude of the RF trapping field is zero along the centerline and increases, with radius, to a maximum value near the rods.

As the number of ions temporally varies in a small range about a target value, space-charge repulsion causes the ensemble of ions to occupy a varying volume within the trap. The change in radial occupation results in a change in the time-averaged magnitude of the trapping RF field sampled by the ions and a change in ion micromotion amplitude, which will cause a corresponding change in the second-order Doppler shift. (The first-order Doppler shift is eliminated by the geometry of the trap and the polarization of interrogating microwave field.)

In a 12-pole trap, the ions are free particles for most of their trajectories, interacting with significant RF amplitude only at the edges of the trap. As a result, the time-averaged RF amplitude sampled by the ions is significantly smaller, for the same number of ions trapped, than it is in a typical quadrupole trap used in an earlier-generation LITS. The sensitivity to the second-order Doppler shift is more than 10 times smaller than in the case of a quadrupole-trap LITS, making the long-term stability of a 12-pole-trap LITS comparable to or even better than that of the best hydrogen masers. Nevertheless, the second-order Doppler shift remains the largest shift in the LITS, and the problem is to reduce it even further.

As a solution to this problem, the present compensation scheme exploits the following facts:

  • The ion-number-dependent second-order Doppler shift is negative and increases in magnitude as the number of ions increases.
  • Heretofore, in designing a LITS, great care has been taken to provide a uniform magnetic field within the trap so that as the volume occupied by the ions changes, the average magnetic field sampled by the ions does not change.
  • Notwithstanding the nominal uniformity of the magnetic field as described above, it is possible to introduce a well-controlled magnetic-field inhomogeneity, such that ions in a changing occupation volume sample a slightly different magnetic field. The resulting inhomogeneity in the second-order Zeeman shift can be used to counteract the second-order Doppler shift.