We investigate non-Hermitian Hamiltonian which governs system includes two-level atom and electromagnetical field with circular polarization vector. We find the Hamiltonian by using the 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 Schr\"{o}dinger equation in pseudo interaction picture, we show that our results and the results of JC Hamiltonian are in excellent agreement.}
