由于其独特的物理特性及潜在的应用前景，近年来凝聚超冷量子气体的研究引起了人们的极大关注。本项目将开展凝聚超冷量子气体中弱光孤子形成与传播特性的研究，内容包括：(1) 根据奇异摄动理论，建立研究光与凝聚超冷量子气体相互作用的理论方法，系统地计算由光子和物质波相互作用引起的各阶非线性光学极化率；(2) 基于超辐射散射模型，研究凝聚超冷量子气体中弱光孤子的形成与传播，通过将凝聚体的结构因子引入散射场的Maxwell方程，解释凝聚超冷量子气体中散射场产生的物理机制；(3) 研究量子干涉效应对弱光孤子传播特性的影响,并探讨在凝聚超冷量子气体中实现高维超慢时空孤子的可能性。该项目的研究对于揭示凝聚超冷量子气体中的新奇非线性与量子效应有重要意义，并且在广义相对论、流体力学现象的类比方面有潜在的应用前景。

Due to their unique physical properties and potential application prospect, in recent years great attention has been paid to the study of condensed ultracold quantum gases. In this project, we shall make the investigation on the properties of formation and propagation of weak-light soliton in condensed ultrcold quantum gases, which include: (1) Develop a theoretical method based on singular perturbation theory to study the interaction between light field and the condensed ultracold quantum gases and calculate every-order optical susceptibilities contributed by the interaction between photon and matter wave in a systematic way. (2) Study the formation and propagation of weak-light soliton in the condensed ultracold quantum gases based on the superradiant scattering model and explain the physical mechanism of the generation of the scattering field by introducing the structure-factor into the Maxwell equation of the scattering field. (3) Study the propagation of weak-light solitons with the effects of quantum interference and explore the possibility of realizing high-dimension spatial-temporal solitons with ultraslow group velocity in condensed ultracold quantum gases. The implementation of this project is of importance for the finding of new nonlinear and quantum effects of condensed ultracold quantum gases and has potential applications in the analogy of phenomenon of the general relativity and the fluid mechanics.