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We describe a broadly applicable experimental proposal to search for theviolation of local Lorentz invariance (LLI) with atomic systems. The new schemeuses dynamic decoupling and can be implemented in current atomic clocksexperiments, both with single ions and arrays of neutral atoms. Moreover, thescheme can be performed on systems with no optical transitions, and thereforeit is also applicable to highly charged ions which exhibit particularly highsensitivity to Lorentz invariance violation. We show the results of anexperiment measuring the expected signal of this proposal using a two-ioncrystal of $^{88}$Sr$^+$ ions. We also carry out a systematic study of thesensitivity of highly charged ions to LLI to identify the best candidates forthe LLI tests.

New ideas for tests of Lorentz invariance with atomic systems