带有无序效应的超冷费米原子气体的物性研究

Ultracold Fermi gases provide a clean and controllable testbed for manybody theories and act as simulators of complex many-particle systems. In particular, ultracold fermions with tunable intractions were used to theoretically and experimentally study the evolution from the BCS superfluid to the Bose Einstein condensate (BEC). This study also has additional promising research directions. For example, recently experimentalists now can create controlled disordered interacting potentials, this makes it possible to study the effects of disorder during BCS-BEC crossover. It further pave the way towards the realization of versatile quantum simulators. In this project, we are going to establish an approximated microscopic framework about the disordered ultracold Fermi gases, which can be used to discuss their physical properties like the phase diagrams and collective excitations. We expect it will produce some interesting and experimentally textable predictions.

超冷费米原子气体为多体理论的研究提供了一个干净可控的实验台，同时也可以作为复杂多粒子体系的实验模拟器，尤其是相互作用可控的超冷费米子同时可以在理论和实验上用于研究多粒子体系从BCS超流到玻色-爱因斯坦凝聚（BEC）的演化。对超冷原子气体的研究还有一些新的相当前景的研究方向，例如目前已经在实验上实现可控的随机、无序相互作用势已经可以实现，这使得研究带有无序效应的BCS-BEC连续过渡成为可能，这有助于我们实现多种多样的量子模拟器。在本项目中，我们希望建立一套可以处理带有无序效应的冷原子体系的近似微观理论框架，以讨论它们的相图以及集体激发等物理性质，我们希望能给出一些有趣并且在实验上可观测的理论预言。

项目组在如下方面取得了一系列进展：一是对一维准周期超冷费米系统的拓扑和动力学性质做了深入研究，尤其是无序现象对这些低维量子系统的拓扑性质的影响；二是对量子代数尤其是q变形代数在超冷费米原子气体体系中的应用、热基态理论在量子多体体系尤其是BCS模型中的应用等做了深入研究，给出了诸如q诱导相变等有趣的理论预言；三是对量子混合态的几何相位和动力学相位物理性质做了深入研究，发现量子混态体系的拓扑相变与动力学相变可以统一用量子保真度在不同过程中的零点来描述。