Coherent Control of Diabolic Points of a Hermitian Hamiltonian in a Four-Level Atomic System Using Structured Light Fields

A four-level atomic medium is used to manipulate the diabolic points of the Hermitian Hamiltonian using driving fields of structured light. The diabolic points of the fourth, third, and second orders are observed by the real and imaginary parts of the eigenvalues of the Hermitian Hamiltonian. The diabolic points and degeneracy regions are studied with variation in Rabi frequencies, detuning, and topological charges. The structured light has a key impact on diabolic points. By changing the topological charges, the number of diabolic points and the degeneracy regions are changing. The imaginary part of eigenvalues shows fourth-order diabolic points. At topological charge ℓ=even, the real part of eigenvalues does not show higher-order diabolic points. The obtained results of the diabolic point are helpful in the fields of deformation space, entanglement physics, optomechanical systems, and crystal optics.