A two-level atom is subject to electromagnetic radiation, which is polarized along the x direction and propagates in the direction. Within the electric dipole approximation, write out the Hamiltonian of the incident electric field and the matrix element that describes the transition between the two atomic levels.

A two-level atom is subject to electromagnetic radiation, which is polarized along the x direction and propagates in the direction. Within the electric dipole approximation, write out the Hamiltonian of the incident electric field and the matrix element that describes the transition between the two atomic levels.