Band Characteristics of a Parity-Time Symmetric Photonic Crystal Made of Multi-Level Atomic Systems

Partity-time symmetry enables a quantum system or an optical/electromagnetic structure to have real eigenvalue spectra of energy (or wave number). A relatively simple and convenient scenario, which takes advantage of multi-level transition and optical pumping in a four-level atomic system, is suggested in order to achieve parity-time symmetry of such an atomic medium. In the present parity-time symmetric atomic vapor, the real part of the obtained electric permittivity is a constant, and the imaginary part is an odd function (e.g., sine function of spatial coordinate). The optical characteristics of such a parity-time symmetric periodic dielectric have also been studied in this paper. It can be found that the Bloch wave numbers in the present periodic dielectric are purely real or purely imaginary. A threshold in the magnitude of the imaginary part of the parity-time symmetric permittivity for emergence of forbidden band is also indicated in our numerical calculation. The present scenario for realizing parity-time symmetric atomic vapor would find potential applications in some new photonic or quantum optical device design and fabrication.