  Lorentz symmetry is one of the cornerstones of modern physics. However, a
number of theories aiming at unifying gravity with the other fundamental
interactions including string field theory suggest violation of Lorentz
symmetry [1-4].
  While the energy scale of such strongly Lorentz symmetry-violating physics is
much higher than that currently attainable by particle accelerators, Lorentz
violation may nevertheless be detectable via precision measurements at low
energies [2]. Here, we carry out a systematic theoretical investigation of the
sensitivity of a wide range of atomic systems to violation of local Lorentz
invariance (LLI). Aim of these studies is to identify which atom shows the
biggest promise to detect violation of Lorentz symmetry. We identify the Yb+
ion as an ideal system with high sensitivity as well as excellent experimental
controllability. By applying quantum information inspired technology to Yb+, we
expect tests of LLI violating physics in the electron-photon sector to reach
levels of $10^{-23}$, five orders of magnitude more sensitive than the current
best bounds [5-7]. Most importantly, the projected sensitivity of $10^{-23}$
for the Yb+ ion tests will allow for the first time to probe whether Lorentz
violation is minimally suppressed at low energies for photons and electrons.
