本项目基于相干共振原子介质，建立探测场满足的具有不同维度、多种形式（包括无序）外势的线性、非线性Parity-time (PT) 对称模型。通过探测场的脉宽和束腰调控维度；利用辅助场、外加磁场以及大失谐激光场构建外势；应用失谐量、场强及原子数密度等参数调节非线性效应。在线性模型中，深入研究维度、无序和外势等因素对PT对称破缺点以及安德森局域态的影响。在非线性模型中，系统讨论不同维度、无序外势及非线性效应下的基阶和高阶孤子稳定性问题。此外还提出一种非线性效应对PT对称破缺点影响的有效分析方法。预期成果可揭示PT对称外势、无序外势以及非线性效应之间相互竞争和合作机理，也将推动PT对称理论在相关领域中的应用。

Based on the coherent resonant atomic media, we will construct the linear and nonlinear Parity-time (PT) symmetrical models with different dimensionality, various exernal potentials (including disorder potential). The dimensionality is controlled by the pulse width and the radius of beam waist. The external potentials will be designed by the assisted field, the magnetic field and the far-detuned laser field. The nonlinear effect can be adjusted by the detuning, the field intensity, and the atomic density. In the linear model, the effects on Anderson localization (AL) and PT symmetry-breaking point caused by the various nonlinearities and disordered external potentials will be studied in different dimensionality. In the nonlinear model, the stability of various types of solitons, including in high-dimensional, low dimensional, ground and high-order solitons, will be explored in detail. We also provide a kind of method to study the influence of nonlinearity on PT symmetry-breaking point. Of importance, our results will reveal the mechanism of interplay among dimensionality, external potential, nonlinearity, PT symmetry, and generlizes the applications of PT symmetry into related fields.