  We propose a scheme to measure a nuclear magnetic quadrupole moment (MQM), a
CP-violating electromagnetic moment that appears in the nuclear sector, using
the long-lived $^3P_2$ metastable state in neutral $^{173}$Yb atoms.
Laser-cooling and trapping techniques enable us to prepare ultracold $^{173}$Yb
atoms in the $^3P_2$ state trapped in an optical lattice or an optical tweezer
array, 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 gradient
generated by the atomic electrons in this state, which amplifies the measurable
effect of an MQM. Our scheme could lead to an improvement of more than one
order of magnitude in MQM sensitivity compared to the best previous measurement
[S. A. Murthy et al., Phys. Rev. Lett. 63, 965 (1989)]
