Structures, Dynamics, and Thermodynamics of Atomic Boson-Fermion Mixtures

原子混合物在我们的日常生活中无处不在。例如，空气是氮气、氧气和其他成分的混合物。冷却空气导致液化，这是多物种混合物结构转变的典型例子。由量子物理学控制的微观世界包含量子粒子的混合物，这些混合物展示了许多等待我们探索的奇异现象。宇宙中有两种原子，玻色子和费米子。它们的区别在于它们的对等相互作用：玻色子倾向于聚集在量子体系中，而费米子则彼此远离。几十年来，关于玻色子和费米子的量子混合物的物理问题一直吸引着科学家。氦原子为探索量子混合物提供了一个平台，然而，复杂的原子相互作用和具有挑战性的实验使系统变得复杂。然而，最近在冷却、捕获和操纵原子方面的进展已经成功地产生了玻色子-费米子量子混合物，并重新引起了人们对这种系统的研究兴趣。拟议的研究将调查的结构，热力学和动力学的新型原子玻色子费米子混合物。解释一下，这项研究将提供（1）量子玻色子-费米子混合物的完整理论，允许详细分析系统的平衡状态和平衡状态，（2）描述玻色子和费米子如何相互推动，形成像空气一样的均匀混合物或像水中的油一样的分离，（3）探索和预测量子玻色子-费米子混合物在不同结构中的动力学行为。此外，虽然不同实验研究小组实现的量子混合物被限制在不同的几何形状中，但拟议的研究将提取普遍的行为并阐明潜在的机制。这些结果将揭示量子玻色子-费米子混合物的新颖结构和动力学，并促进我们对复合量子系统背后的多体物理的理解。多组分混合原子的捕获和操纵技术的迅速发展使得对玻色子-费米子混合体的研究成为一项重要而紧迫的任务，这一研究将及时地描述混合体的结构和动力学。在基于量子场论的研究框架中，原子混合物在均匀或谐波势中的相图将解释当前和未来的实验数据，并指导多物种量子系统中临界现象的研究。通过对混合物空间结构的模拟和分析，可以从平衡态的相分离结构中提取临界指数，通过对量子动力学的分析，可以揭示费米子对玻色超流体中涡旋形成的影响。玻色子-费米子混合物中标度行为的分解将反映一级结构转变，与二级相变的常规分析的比较将揭示临界区域的大小。该研究将与实验组建立合作，以表征不同陷阱几何结构中原子玻色子-费米子混合物的结构，热力学和动力学。理论框架，模拟和结果将指导和解释原子混合物的实验。为了促进研究和倡导公共学习，PI将向少数民族人口众多的当地社区提供公开讲座，并将招募少数民族和女性学生参与研究并增加多样性。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Atomic mixtures are ubiquitous in our daily life. For example, air is a mixture of nitrogen, oxygen, and other ingredients. Cooling down the air leads to liquefaction, showing a typical example of structural transitions in multi-species mixtures. The microscopic world governed by quantum physics contains mixtures of quantum particles that exhibit many exotic phenomena awaiting our exploration. There are two types of atoms in the universe, bosons and fermions. They differ by their peer-interactions: bosons tends to congregate in the quantum regime while fermions stay away from each other. Questions about the physics of a quantum mixture of both bosons and fermions have fascinated scientists for decades. Helium atoms have offered a platform for exploring quantum mixtures, however, the systems are complicated by the complex atomic interactions and challenging experiments. Nevertheless, recent advances in cooling, trapping, and manipulating atoms have successfully produced boson-fermion quantum mixtures and renewed research interest in such systems. The proposed research will investigate the structures, thermodynamics, and dynamics of the novel atomic boson-fermion mixtures. Explicitly, the research will deliver (1) a full theory of the of quantum boson-fermion mixtures, allowing a detailed analysis of the system in and out of equilibrium, (2) a description of how bosons and fermions push each other to form a homogeneous mixture like air or a separation like oil in water, and (3) an exploration and prediction of the dynamics of quantum boson-fermion mixtures driven across the different structures. Moreover, while the quantum mixtures realized by different experimental research groups are confined in different geometries, the proposed research will extract the universal behavior and elucidate the underlying mechanism. The results will reveal the novel structures and dynamics of quantum boson-fermion mixtures and advance our understanding of the many-body physics behind composite quantum systems. The rapid developments of trapping and manipulating multi-species atomic mixtures have made the investigation of boson-fermion mixtures an important and urgent task, and the research will deliver a timely description of the structures and dynamics of the mixtures. The phase diagrams of atomic mixtures in uniform or harmonic potentials from the framework developed in the research based on quantum field theories will explain the current and future experimental data and guide the investigations of critical phenomena in multi-species quantum systems. The simulations and analysis of the spatial structures of the mixtures will demonstrate the extraction of critical exponents from a phase-separated structure in equilibrium, and the analysis of the quantum dynamics will reveal the influence of the fermions on the vortex formation in the bosonic superfluid. The breakdown of the scaling behavior in boson-fermion mixtures will reflect the first-order structural transition, and a comparison with the conventional analyses across a second-order phase transition will reveal the size of the critical regime. The research will establish collaborations with experimental groups to characterize the structures, thermodynamics, and dynamics of atomic boson-fermion mixtures across structural transitions in different trap geometries. The theoretical framework, simulations, and results will guide and explain experiments of atomic mixtures. To promote the research and advocate public learning, the PI will present public lectures to the local communities that have high populations of under-represented minorities and will recruit minority and women students to participate in the research and increase diversity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.