  We propose to detect quadrupole interactions of neutral ultra-cold atoms via
their induced mean-field shift. We consider a Mott insulator state of
spin-polarized atoms in a two-dimensional optical square lattice. The
quadrupole moments of the atoms are aligned by an external magnetic field. As
the alignment angle is varied, the mean-field shift shows a characteristic
angular dependence, which constitutes the defining signature of the quadrupole
interaction. For the $^{3}P_{2}$ states of Yb and Sr atoms, we find a frequency
shift of the order of tens of Hertz, which can be realistically detected in
experiment with current technology. We compare our results to the mean-field
shift of a spin-polarized quasi-2D Fermi gas in continuum.

Quantum Gases;Quantum Physics