Non-Hermitian interaction of matter and light

We investigate the non-Hermitian Hamiltonian which governs the system including two-level atom and electromagnetical field with a circular polarization vector. We find the Hamiltonian by using dipole approximation and rotating wave approximation (RWA), which lead to a non-Hermitian Hamiltonian. We solve the time-independent non-Hermitian Hamiltonian and obtain real eigenvalues of energy for this system. Finally, by solving the Schroedinger equation in the pseudo interaction picture, we show that our results and the results of Jaynes-Cummings (JC) Hamiltonian are in excellent agreement