相干共振原子介质中光的安德森局域化

In this application, we will carry out Anderson localization (AL) of light in the coherent resonant atomic medium, including: (1) Based on the resonant interaction between light and multi-levels atomic medium, the Anderson model with various nonlinearities and disordered potentials will be set up , and one-dimensional, two-dimensional, and three-dimensional models will be obtained under the different physical conditions. Here, the disordered external potentials include the combination of a periodic potential with a random external potential, corresponding to the doped crystal, the quasi-periodic external potential corresponding to the quasicrystal, and the random external potential corresponding to the amorphous. And the nonlinearities include the self-focusing Kerr nonlinearity, the defocusing Kerr nonlinearity, the cubic-quintic nonlinearity, and the saturable nonlinearity. (2) In the different dimensions, the effects on the localization extent and stability of AL caused by the interaction between various nonlinearities and disordered external potentials will be studied, and the best experimental projects to realize AL will be proposed. (3) In different dimensions, the formation of solitons affected by various disordered potentials will be studied, and the plan to stabilize and control solitons by disordered potentials can be obtained. In this project, some solid physical phenomena will be shown in the coherent resonant atomic medium, the expected results will not only reveal the mechanism of the mutual competition and cooperation between nonlineaities and disordered potentials in the process of the different dimensional AL, and provide a feasible experimental program to realize AL, but also promote the applications of AL to some correlated research areas in the condensed matter physics.

本项目开展在相干共振原子介质中实现光的安德森局域化研究，内容包括：（1）建立基于光与多能级原子共振相互作用的、具有不同无序外势和非线性形式的安德森模型，在不同物理条件下实现有关的一维、二维、三维模型。其中无序外势包括相应于晶体掺杂的周期外势与随机外势的叠加、相应于准晶的准周期外势和相应于非晶的完全随机外势；非线性形式包括自聚（散）焦克尔、三-五次、多种饱和等。（2）研究不同维度下各种无序外势与非线性的相互作用对安德森局域态的局域程度、稳定性等的影响，提出在相干共振原子介质中实现安德森局域的最优实验方案；（3）研究不同维度下各种无序外势对孤子形成的影响，给出利用无序外势控制、稳定孤子的方案。本项目应用相干共振原子介质模拟固体物理现象，预期成果可揭示各维度下安德森局域态形成过程中无序与非线性相互竞争、合作的机理，为安德森局域化现象的实现提供可行方案，可推动其在凝聚态物理相关研究领域中的应用。

本项目在相干原子介质中构建了Anderson模型，并研究了局域态的特性。具体研究内容如下：.（1）基于光与多能级原子共振相互作用的电磁感应透明（EIT）与主动拉曼增益系统，构建了多种模型。包括具有多种外势形式的Aubry-Andre（AA）模型；周期与无序叠加外势或完全随机外势的Anderson模型，且该模型中可包含自聚焦Kerr、自散焦Kerr、三—五次、饱和等非线性相互作用中的任一种。在此基础上也模拟了光场满足的Parity-time对称模型，场论中的Thirring模型以及高维时空光孤子满足的非线性薛定谔方程。. （2）研究了维度、非线性、外势形式对局域态的影响。在AA模型中，我们发现可以通过调节准周期外势的形式来改变局域态的分布以及波形；并且维度不改变扩展态向局域态转变的相变点，但高维体系中局域态更局域；非线性相互作用对局域态的相变点无影响，但是自聚焦相互作用有利于局域，自散焦相互作用不利于局域。在周期加随机的Kerr非线性、三—五次非线性Anderson模型中，都是自聚焦有利于局域，自散焦不利于局域。.（3）研究了无序对孤子的影响，以及局域态与孤子之间的关系。我们发现无序外势并不影响孤子的存在。在周期加随机外势的具有各种非线性相互作用的Anderson模型中，发现了各种孤子的轮廓图，并讨论了他们的稳定性。并且在Parity-time对称模型中，发现非线性局域态孤子与线性局域态孤子之存在着一定的关联。.总之，该项目借助相干原子介质模拟了固体物理中的Anderson局域现象，揭示了维度、非线性相互作用、外势形式等各个因素对局域态的影响，也给出了无序外势对孤子的作用，并探讨了局域态与孤子之间的内在联系。.