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

作为量子力学的基本原理之一的泡利原理指出，相同的费米子不可能同时占据相同的量子态。这一简单的声明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，但它的证据仍然难以捉摸。泡利原理强调微观和宏观物质的稳定性，控制从超冷费米气体到热中子星的所有长度和温度范围内的现象。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(如过度流动)中的作用。早期的研究表明，保利原理在集体行为的出现中发挥了比预期更大的作用。了解这种有组织的行为很重要，因为它可以用来开发用于量子信息处理的工程化量子系统、量子增强型传感器和高温超导体，这些可能会给电气工程应用带来革命性的变化。这个项目描述了一个计划，研究在从复杂的微观运动到简单的集体行为(如在超流体材料中看到的)的动态转变过程中所起作用的力。特别是，PI计划研究Pauli原则在有组织行为的创造和稳定中的作用。实验学家在实验室中制造出了超冷费米子的受控系统，展示了普遍的集体性质。这个项目的目标是在集体行为出现时从理论上研究这些系统，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。PI计划使用多体微扰方法，利用群论技术获得一阶解析简正模的解，研究这些简正模的特征的演变，并监测最近测量的性质，包括激发频率和热力学参数，随着系统参数接近支持集体行为的么正区域。这项工作可以促进我们生产和控制这些系统的能力，并提高它们在技术上的使用。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.