quantum mechanics - Can atoms have nonzero dipole moments?

Let's make the question easier by considering two-level atoms(with spin states, i.e. spin up $|\uparrow\rangle$ and spin down $|\downarrow\rangle$). An article I recently read claims that atoms do not have dipole moments when they are in energy eigenstates (i.e. when you put it into a magnetic field in z direction).

I was thinking if it's an eigenstate, since the spin cannot be pointing in z direction (remember it's actually pointing in a cone area), how could it not have a dipole moment?