Electromagnetically Induced Grating In A Multi-level Cold Atomic System By Using Laplace Transform Method

In recent years,electromagnetically induced transparency and electromagnetically induced grating based on quantum coherence and quantum interference in the field of the interaction light and atomic system have attracted attention of many researchers.Electromagnetically induced transparency is using a weak probe beam and a strong coupling beam on the atomic system,and then the absorption of the detection light by the medium will decrease or even decreases to zero,presenting a transparent window.Based on the electromagnetically induced transparency,using the standing wave field replaced the traveling wave field,the grating similar to Fraunhofer far-field diffraction will be appeared in atomic media,which is called electromagnetically induced grating.The main work in the paper is:1.Introduced two methods of solving the absorption coefficient and refraction coefficient,and the first one is to obtain the density matrix motion equation of the system by using the rotating-wave approximation and Probability amplitude method in the interaction picture,and then solve the absorption coefficient and refraction coefficient of the steady state.The second one is based on the equation of the density matrix motion,and the absorption coefficient and refraction coefficient are solved by using the Laplace transform method.2.Based on electromagnetically induced transparency,we simulated electromagnetically induced grating in the three-level ?-type atomic system and the four-level N-type atomic system,with 22.22% and 29% for the first order diffraction efficiency,respectively.In the actual experiment and application,the energy level of the atom is more complex,so we extended the energy level structure to the six-level structure.In the six-level ?-type atomic system,we simulated the electromagnetically induced grating,and analyze the influence of each parameter on the first order diffraction.Then we selected the appropriate parameter,and obtained the first order diffraction efficiency is 16.87%.3.In order to seek higher diffraction efficiency in the complex atomic energy level,we considered adding a field on the six-level ?-type atomic system,which formed six-level N-type atomic model.Considering that the excited state energy levels are close to each other and two fields are added at the same time,the absorption coefficient and refraction coefficient cannot be directly solved,so we used the Laplace transform method to solve the absorption coefficient and refraction coefficient,and on this basis,simulating the phenomenon of electromagnetically induced grating,and obtaining two types of six-level N-type atomic models.The effect of each parameter on the first-order diffraction efficiency was analyzed.When fields were added between 13 and 24 energy levels,the first-order diffraction efficiency was 33.78%,which was very close to the ideal phase grating(34%).When combined with fields between level 13,25,got the first order diffraction efficiency is 27%,based on this and four-level N-type atomic system were compared with six-level ?-type atomic system.According to the results,we used two methods to solve the absorption coefficient and refractive index,and we got electromagnetically induced grating on the basis.The first order diffraction efficiency of electromagnetically induced grating in six-level N-type atomic system is higher than that of four-level N-type atomic system and sixlevel ?-type atomic system by using the method of Laplace transform.It provided a theoretical basis for relevant experiments and researches.