MINIMIZING THE TIME-DILATION SHIFT IN PENNING TRAP ATOMIC CLOCKS

If environmental perturbations are made negligible, the time-dilation shift is expected to give one of the largest systematic uncertainties in a stored ion clock. In general, this shift increases with the numbe r of trapped ions. Fluctuations in the time dilation shift therefore c ould limit the frequency stability of an ion clock. We show that in a Penning trap, relativistic time dilation can be minimized if the laser -cooled ions are prepared in a special spheroidal state. In addition, a modest stabilization of the spheroid near the minimum-shift configur ation can significantly reduce fluctuations in the time dilation. The results obtained for a single-species ion clock also provide a good ap proximation for a sympathetically cooled system.