Covalent and photonic interactions between atoms in lattice are controlled by probe absorption and dispersion spectrums. Similarly, information of covalent interaction among atoms within a crystal is extracted by absorption and dispersion spectrums in the range of \(-2\pi \le kx,ky \le 2\pi\) . Localization of atoms and pairs of electron density are controlled by the gradients ( \(\partial n_r / \partial x\) and \(\partial n_r / \partial y\) ) variation of absorption and dispersion spectrums of the four-level atomic medium. Additionally, the covalent interaction between atoms are modified using structured light beams in the range of \(-3 \mu m \le x,y \le 3\mu m\) . The sharing of electrons between atoms are controlled and modified by the parameters of probe, control fields and the gradients variation of absorption and dispersion. This work will play an important role in the field of quantum enhanced metrology, trapping of atoms, nanolithography and Bose-Einstein condensate.
