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We propose a scheme to measure a nuclear magnetic quadrupole moment (MQM), aCP-violating electromagnetic moment that appears in the nuclear sector, usingthe long-lived $^3P_2$ metastable state in neutral $^{173}$Yb atoms.Laser-cooling and trapping techniques enable us to prepare ultracold $^{173}$Ybatoms in the $^3P_2$ state trapped in an optical lattice or an optical tweezerarray, providing an ideal experimental platform with long spin coherence time.In addition, our relativistic configuration interaction calculation for the$^3P_2$ electronic wavefunction reveals a large magnetic field gradientgenerated by the atomic electrons in this state, which amplifies the measurableeffect of an MQM. Our scheme could lead to an improvement of more than oneorder of magnitude in MQM sensitivity compared to the best previous measurement[S. A. Murthy et al., Phys. Rev. Lett. 63, 965 (1989)]

Measuring the nuclear magnetic quadrupole moment of optically trapped ytterbium atoms in the metastable state