| In recent years, due to the investigation activities of electromagnetically in-duced transparency (EIT), the propagation of lights in resonant atomic media has attracted a lot of interests. The idea of EIT is that it introduces an extra control field to induce a quantum interference between the atomic states, which can be used to eliminate the absorption of a probe field propagating in the media. In the presence of EIT, the dispersion properties of the system will change greatly, which leads to a significant reduction of the group velocity of the probe field. This striking feature can be used to develop new optical delay devices and realize the storage and retrieve of optical information in atoms. In the same time, a dramatic enhancement of Kerr nonlinearity can be found in active EIT media, due to the resonantly interaction between light and materials. This striking feature can be used to realize the high efficient four-wave mixing and to develop new all-optical logic gates. Although the research of EIT has been last for more than20years, the realization of EIT in practical systems is still an open question. For example, what is the difference between the EIT in a closed atomic system and that in an open atomic system; how the warm atoms influence the EIT, etc. These topics need more studies.On the other hand, due to the inherent dispersion of the EIT media, the laser pulses propagating in the media usually suffer a serious deformation, which will greatly decrease the fiedility of the information. However, one can use the en-hanced nonlinearity of the media to balance the dispersion. In this way, the laser pulse will form optical solitons and propagate for a long distance without suf-fering serious deformation. Further, such kind of optical solitons can propagate with ultraslow velocity compared with the light speed in vacuum, and hence they are called ultraslow optical solitons. They can also be generated with very low input power. The ultraslow optical solitons have potential applications in optical information processing and transmission.In this work, we plan to study:(1) We shall derive the Maxwell-Bloch equation for the A-type three-level sys-tem under the semi-classical theory. The linear optical response for both closed and open systems will be analyzed. A comparison will be made.(2) We shall study the EIT in a tripod system with cold atoms. From the Maxwell-Bloch equation, we shall study the linear optical response and find that the linear dispersion relations of the two probe fields in the tripod system are independent. Whereas, their group velocities can be greatly reduced and well matched. We shall also study the EIT in a tripod system with warm atoms. The results will be compared with those reported by MacRae et al in Ref.[48].(3) We shall study the formation and propagation of ultraslow optical soli-ton pairs in the tripod system. From the Maxwell-Bloch equation, we shall derive the coupled nonlinear Schrodinger equations by using a standard multiple-scales method. A set of practical parameters provided in [48] and numerical simulations will be used to test the stability of such ultraslow optical soliton pairs. The inter-action between two solitons will be studied. Lastly, the influence of the Doppler broadening on ultraslow optical soliton pairs will be studied.The results presented in this work may be useful for the fundamental theory of nonlinear optics in coherent media, guiding a relevant experiment, and having potential applications in a future technology. |
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