Superfluid Atomic Bosons, Fermions and Their Mixtures

超冷原子物理领域一直在快速发展，没有放缓的迹象。在这个奖项下，我们将对有关冷原子超流性质的几个重要问题进行理论研究。这些项目具有根本性的重要性，同时也受到该领域最近的实验进展的启发。我们将考虑冷原子系综的性质，它们所在的有效空间维度是可调的。可调的空间维度在其他材料中是不容易实现的。但对于冷原子，通过调整用于限制它们的囚禁势的几何形状，这样的壮举可以在实验室中实现。我们还将考虑冷原子在适当安排的激光场的操纵下的新性质。在适当的条件下，激光可以感应合成电磁场，使中性原子的行为就像带电粒子在电场和/或磁场中运动一样。这些研究项目与目前的实验非常相关，其中一些实验是由Pi在莱斯大学的同事进行的。这些问题跨越了冷原子领域中相当广泛的范围，与凝聚态物理和非线性物理密切相关。参与这些项目的学生将接受理论物理方面的扎实培训，包括分析方法和数值技术。这样的培训对他们未来的科学和工程职业生涯将非常有价值。

The field of ultracold atomic physics has been progressing rapidly without signs of slowing down. Under this award, we will carry out a theoretical study of several important problems concerning the superfluid properties of cold atoms. These projects are of fundamental importance, and in the meantime are inspired by recent experimental progress in the field. We will consider the properties of cold atomic ensembles whose effective spatial dimensions in which they live are tuned. A tunable spatial dimension is not readily achievable in other materials. But for cold atoms, by adjusting the geometry of the trapping potential that is used to confine them, such a feat can be realized in the lab. We will also consider the novel properties of cold atoms under the manipulation of appropriately arranged laser fields. Under proper conditions, the laser beams can induce synthetic electromagnetic fields such that the neutral atoms behave like charged particles moving in electric and/or magnetic fields. These research projects are of great relevance to current experiments, some of which are being carried out by PI's colleagues at Rice University. These problems span a quite wide spectrum within the field of cold atoms with close ties to condensed matter physics and nonlinear physics. Students involved in these projects will receive a solid training in theoretical physics, including both analytical methods and numerical techniques. Such a training will be very valuable for their future career in science and engineering.