New Methods for Testing Lorentz Invariance with Atomic Systems

We describe a broadly applicable experimental proposal to search for the violation of local Lorentz invariance (LLI) with atomic systems. The new scheme uses dynamic decoupling and can be implemented in current atomic clock experiments, with both single ions and arrays of neutral atoms. Moreover, the scheme can be performed on systems with no optical transitions, and therefore it is also applicable to highly charged ions which exhibit a particularly high sensitivity to Lorentz invariance violation. We show the results of an experiment measuring the expected signal of this proposal using a two-ion crystal of ${}^{88}{\mathrm{Sr}}^{+}$ ions. We also carry out a systematic study of the sensitivity of highly charged ions to LLI to identify the best candidates for the LLI tests.

Figure 1

Theoretical calculation of $P_{7/2,m}(\kappa T,\varphi )$ for different $m$ values. $P_{7/2,m}$ is periodic in $\kappa T$ with a period of $\pi$, and it is symmetric with respect to $\pm m$. Therefore, we plot only negative $m$ values and $\kappa T\in [0,\pi ]$. (a),(b) Theoretical calculation of $P_{7/2,-7/2}(\kappa T,\varphi ),P_{7/2,-1/2}(\kappa T,\varphi )$ as a function of $\varphi$ and $\kappa T$, respectively. The solid red line marks the $\varphi =\pi$ line, where the Ramsey fringe should be measured for maximal sensitivity. (c),(d) Ramsey fringe in the $m=-\frac{7}{2},-\frac{1}{2}$, respectively, as a function of $\kappa T$. The curves correspond to the populations along the red solid lines in the (a) and (b) plots, respectively. The red dashed line marks the highest sensitivity $\kappa T$, and the red full circle marks the corresponding value of $P_{J,m}(\kappa T,\varphi )$.

Figure 2

Experimental verification of the DD method on the $4D_{5/2}$ level of two trapped ${}^{88}{\mathrm{Sr}}^{+}$ ions. (a),(b) The measurement of $P_{5/2,-3/2}(\kappa T,\varphi )$ in percent after the above DD sequence for different $T$ and $\varphi$, for ion 1 and ion 2, respectively. In the experiment, $t_w=150\mu \mathrm{s}$ and the DD pulse number goes from 2 to 110 (see Supplemental Material [13]). (c) The theoretical calculation of $P_{5/2,-3/2}(\kappa T,\varphi )$.