Conical diffraction and Floquet edge states in an electromagnetically induced Lieb lattice

we investigate conical diffraction and Floquet edge states in a Lieb photonic lattice induced in a Λ-type atomic system with electromagnetically induced transparency. By tuning frequency detuning and coupling field intensity, we demonstrate significant modifications to both the Bloch structure and the resulting diffraction patterns. Furthermore, we theoretically model a helical Floquet modulation to break time-reversal symmetry, resulting in a photonic topological insulator. Through detailed theoretical and numerical analyses, including calculations of Berry curvature and Chern numbers, we verify the emergence of unidirectional edge states and their robustness against defects. These findings highlight the potential for dynamically controlling beam propagation in atomic lattices and open promising avenues for designing advanced photonic devices with topological protection.