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

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 $\Lambda$-type level configuration. A linewidth of $\approx 114\text{MHz}$ 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 $\left|{\widehat{\alpha }}_2\right|<1.2\times {10}^{-5}$, a $25\times$ tighter limit on $O\mathbf{\left(}{\left(v/c\right)}^4\mathbf{\right)}$ deviations from time dilation than any other experiment.

Figure 1

Left: level scheme of the metastable ${{}^7\text{L}\text{i}}^{+}$ ion containing a closed two-level (dashed line) and three-level $\left(\Lambda \right)$ system (solid lines). Right: scan across the two-level transition with the counterpropagating laser beam at ${\nu }_a\sim 780\text{nm}$.

Figure 2

(Color online) Schematic view of the experimental setup at the ESR. The laser light is provided by a laser diode (LD) and a frequency-doubled titanium sapphire laser; it is guided via fibers to the storage ring (FPI: Fabry-Perot-Interferometer; PD: photodiode; SHG: second-harmonic generation; EOM: electro-optic modulator; AOM: acousto-optic modulator).

Figure 3

$\Lambda$ resonances versus detuning of the scanning diode laser observed (a) with both lasers counterpropagating and (b) with one copropagating and one counterpropagating laser with respect to the ion beam. The solid lines represent Lorentz fits.

Figure 4

Upper limits for deviations of high velocity Ives-Stilwell experiments from the prediction of SR as a function of ${\beta }^2$. The solid dots are limits for $\left|ϵ\left({\beta }^2\right)\right|$ deduced in previous experiments at the TSR [10, 24] and in the present investigation at the ESR. The dashed and dotted curves are limits obtained from previous results when including terms of up to the order $O\left({\beta }^2\right)$ and $O\left({\beta }^4\right)$, respectively, in the expansion of $ϵ\left({\beta }^2\right)$ [see Eq. (4)]. The thick solid line is the limit implied by combining the TSR result with the result of the present measurement; the resulting restriction for the expansion parameters $\widehat{\alpha }$ and ${\widehat{\alpha }}_2$ are shown in the inset. The limits marked by H and $\mu$ are obtained from a Doppler shift experiment on H [33] and a lifetime measurement of the muon [34] when interpreting $ϵ\left({\beta }^2\right)$ within the RMS test theory.