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 number of trapped ions. Fluctuations in the time dilation shift therefore could 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 configuration fan significantly reduce fluctuations in the time dilation. The results obtained for a single-species ion clock also provide a good approximation for a sympathetically cooled system.<>