Population Distribution and Splitting Nonlinearity for Rydberg Atomic Gas under Multiple Fields

Rydberg atom has a very large polarizability proportional to n⁷ (n is the principal quantum number), the energy interval between adjacent energy levels is in the microwave frequency band, and the transition between adjacent energy levels has a huge dipole moment proportional to n⁴; as a result, the Rydberg atom is extremely sensitive to the external field, making it an important means of microwave detection. The interaction of Rydberg atoms with laser fields can be described within the framework of density matrix theory. In this paper, based on a four-level system with multiple laser fields, we study the relationship between the population distribution of different energy levels and the detuning of the coupling field, as well as the effect of the Rabi frequency of microwave field on the electromagnetically induced transparency (EIT) signal by solving the density matrix of the steady state system. Considering the characteristics of density matrix, we assume that the diagonal elements are real and the off-diagonal elements are complex. We find that the operation efficiency of this construction method is twice as high as that of the direct representation by complex numbers. At the same time, we obtain that the Rabi frequency of microwave electric field is proportional to the splitting of EIT signal within a certain range.