Sub-Doppler laser spectroscopy on relativistic beams and tests of Lorentz invariance

Abstract

We demonstrate sub-Doppler laser spectroscopy with a beam of ${^{7}\text{L}\text{i}}^{+}$ ions stored at 33.8% of the speed of light in the experimental storage ring at GSI. Using two lasers, the one copropagating and the other counterpropagating, with respect to the ion beam, a fluorescence line is observed via optical-optical double-resonance spectroscopy on a $\ensuremath{\Lambda}$-type level configuration. A linewidth of $\ensuremath{\approx}114\text{ }\text{MHz}$ is found, which is 12 times narrower than the Doppler broadening due to the momentum spread of the ion beam. Interpreted as a test of Lorentz invariance, we find $|{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\alpha}}}_{2}|<1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, a $25\ifmmode\times\else\texttimes\fi{}$ tighter limit on $O\mathbf{(}{(v/c)}^{4}\mathbf{)}$ deviations from time dilation than any other experiment.