Analysis of thermal radiation in ion traps for optical frequency standards

In many of the high-precision optical frequency standards with trapped atoms or ions that are under development to date, the ac Stark shift induced by thermal radiation leads to a major contribution to the systematic uncertainty. We present an analysis of the inhomogeneous thermal environment experienced by ions in various types of ion traps. Finite element models which allow the determination of the temperature of the trap structure and the temperature of the radiation were developed for five ion trap designs, including operational traps at PTB and NPL and further optimized designs. Models were refined based on comparison with infrared camera measurement until an agreement of better than 10% of the measured temperature rise at critical test points was reached. The effective temperature rises of the radiation seen by the ion range from 0.8 K to 2.1 K at standard working conditions. The corresponding fractional frequency shift uncertainties resulting from the uncertainty in temperature are in the 10^-18 range for optical clocks based on the Sr⁺ and Yb⁺ E2 transitions, and even lower for Yb⁺ E3, In⁺ and Al⁺. Issues critical for heating of the trap structure and its predictability were identified and design recommendations developed.