Normal Modes, Multiplicities, and Superfluidity: The Role of the Pauli Principle in Organizational Collective Phenomena

泡利原理是量子力学的基本原理，指出相同的费米子不能同时占据相同的量子态。 这个简单的命题对我们宇宙的稳定性有着深远的影响，尽管有压倒性的实验证据支持它，但它的证明仍然难以捉摸。泡利原理是微观和宏观物质稳定性的基础，控制着从超冷费米气体到热中子星的所有长度和温度尺度的现象。 在这项研究中，PI建议研究泡利原理在创造和稳定集体行为（如超流性）中的作用。 早期的研究表明，泡利原理在集体行为的出现中发挥了比预期更大的作用。 理解这种有组织的行为很重要，因为它可以用于开发量子信息处理的工程量子系统，量子增强传感器和高温超导体，这些系统可以彻底改变电气工程应用。 该项目描述了一个计划，以调查在从复杂的微观运动到简单的动态过渡过程中发挥作用的力量，如在超流体材料中看到的集体行为。特别是，PI计划研究泡利原理在有组织行为的创造和稳定中的作用。 实验学家已经在实验室中制造出了超冷费米子的受控系统，它们表现出普遍的集体性质。该项目的目标是从理论上研究这些系统，因为集体行为的出现，阐明这种出现背后的驱动力，并提出在实验室中产生和控制集体行为的新方法。 使用多体微扰方法，使用群论技术，以获得分析正常模式的解决方案，在一阶，PI计划研究这些正常模式的字符的演变和监测最近测量的属性，包括激发频率和热力学量的系统参数接近单一的制度，这是众所周知的支持集体行为。这项工作可以促进我们生产和控制这些系统的能力，并提高它们在技术中的使用。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

The Pauli principle, a fundamental tenet of quantum mechanics, states that identical fermions cannot occupy the same quantum state simultaneously. The proof of this simple statement, which has profound implications for the stability of our universe, has remained elusive despite overwhelming experimental evidence supporting it. The Pauli principle underlies the stability of both microscopic and macroscopic matter, controlling phenomena at all length and temperature scales from ultracold Fermi gases to hot neutron stars. In this research, the PI proposes to study the role of the Pauli principle in the creation and stabilization of collective behavior such as superfluidity. Earlier work has suggested that the Pauli principle plays a larger role than expected in the emergence of collective behavior. Understanding such organized behavior is important because it could be used to develop engineered quantum systems for quantum information processing, quantum-enhanced sensors and high temperature superconductors that could revolutionize electrical engineering applications. This project describes a plan to investigate the forces in play during the dynamic transition from complex microscopic motion to simple, collective behavior such as seen in superfluid materials. In particular, the PI plans to study the role of the Pauli principle in the creation and stabilization of organized behavior. Experimentalists have produced controlled systems of ultracold fermions in the laboratory that exhibit universal collective properties. The goal of this project is to study these systems theoretically as collective behavior emerges, to elucidate the driving forces behind this emergence and to propose new ways to produce and control collective behavior in the laboratory. Using a many-body perturbation method that uses group theoretic techniques to obtain analytic normal mode solutions at first order, the PI plans to study the evolution of the character of these normal modes and monitor recently measured properties including excitation frequencies and thermodynamic quantities as system parameters approach the unitary regime which is known to support collective behavior. This work could facilitate our ability to produce and control these systems and enhance their use in technology.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.