“…The ability to develop more precise optical frequency standards will open ways to improve Global Positioning System (GPS) measurements and tracking of deep-space probes, perform more accurate measurements of the physical constants and tests of fundamental physics such as searches for nonlinearity of quantum mechanics, gravitational waves, etc. Some of the promising candidates for such ultra-high-precision frequency standards with trapped ions are 27 Al + [2,3], 199 Hg + [4,5], 171 Yb + [6,7], 87 Sr + [8,9], 43 Ca + [10], 115 In + [11], and 137 Ba + . One of the largest sources of systematic errors in such frequency standards with monovalent ions is due to interaction of the quadrupole moments of metastable states with stray electric field gradients [12,13].…”