A number of theories aiming at unifying gravity with other fundamental interactions, including field theory, suggest the violation of Lorentz symmetry(1-3). Whereas the energy scale of such strongly Lorentz-symmetry-violating physics is much higher than that attainable at present by particle accelerators, Lorentz violation may nevertheless be detectable via precision measurements at low energies(2). Here, we carry out a systematic theoretical investigation to identify which atom shows the greatest promise for detecting a Lorentz symmetry violation in the electron-photon sector. We found that the ytterbium ion (Yb+) is an ideal system with high sensitivity, as well as excellent experimental controllability. By applying quantum-information-inspired technology to Yb+, we expect tests of local Lorentz invariance (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(4-6).