A new test of relativistic time dilation with laser spectroscopy of heavy ions in a storage ring

We report on a new, improved test of time dilation in special relativity via the relativistic Doppler-effect. An optical transition with rest-frequency $\nu$ in $^7{\rm Li}^+$ ions, stored at a speed of $\beta=0.065$ in the TSR heavy-ion storage ring in Heidelberg, was used. The Doppler-shifted excitation frequencies $\nu_{\rm p}$ and $\nu_{\rm a}$ for laser beams travelling parallel and antiparallel with respect to the ions were measured simultaneously using saturation spectroscopy. The resonance conditions $\nu=\gamma (1-\beta)\nu_{\rm p}$ and $\nu=\gamma (1+\beta)\nu_{\rm a}$ yield the relation $\nu_{\rm p} \nu_{\rm a} = \nu ^2$, if $\gamma = \sqrt{1-\beta ^2}$, as predicted by SR. Deviations, e.g. caused by the existence of preferred frames, are parametrized by $\gamma = \gamma_{\rm SR} (1+\alpha \beta^2 + ...)$. We have determined a new limit of $\alpha < 2.2 \times 10^{-7}$, a $10\times$ improvement over other techniques. This result is limited by the knowledge of $\nu$, and not by the accuracy of our measurement. Our new measurement at $\beta = 0.025$ will serve as an improved rest-frequency measurement and will improve the limit on $\alpha$ further.