1 D lattice optical trap via magneto-optical rotation in a bi-refringent medium

We investigate the magneto-optical rotation (MOR) in a one-dimensional optical lattice with birefringence. Hence, we consider a four-level atomic system with two double-degenerated ground states driven by left and right circularly polarized light (LCL/RCL) and controlled via two intense lasers. The trapped atoms typically follow a Gaussian distribution where the control field is modulated with a sinusoidal function oscillating with the lattice period and phase shift. Thus, we perform a quantum control on the (MOR) and shape the transmission/absorption spectra in the lattice. We observe that the external magnetic field affects the rotation of the polarization plane, causing a distinct shift in the MOR, which we attribute to an induced anisotropy. The control field strongly manipulates the dipole moment alignment in the intermediate transition, which leads to a clockwise MOR of -13rd. Besides, the 1D optical lattice exhibits a centralized anisotropy around x = 0 in contrast to an isotropic behavior far from the center. Hence, we achieve selective transmission/ absorption peaks of light, resulting in a honeycomb-like behavior of the LCL/RCL, effectively blocking or transmitting light. Finally, our results are of interest in the area where it is necessary to engineer 1D lattice to exhibit either isotropic or anisotropic behavior with selective transmission/ absorption of light and tailored filtering based on polarization.