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

正则模态、多重性和超流动性：泡利原理在组织集体现象中的作用

• 批准号: 2011384
• 负责人: Deborah Watson
• 金额: $ 12万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2011384&HistoricalAwards=false
• 关键词: Normal; Modes; Multiplicities; Superfluidity; Role

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.

泡利原理是量子力学的基本原理，它指出相同的费米子不能同时占据相同的量子态。 尽管有压倒性的实验证据支持这一简单陈述，但它对我们宇宙的稳定性具有深远的影响，其证明仍然难以捉摸。 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 提议研究泡利原理在超流动等集体行为的创造和稳定中的作用。 早期的研究表明，泡利原理在集体行为的出现中发挥着比预期更大的作用。 了解这种有组织的行为非常重要，因为它可以用于开发用于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，从而彻底改变电气工程应用。 该项目描述了一项计划，研究从复杂的微观运动到简单的集体行为（如超流体材料中所见）的动态转变过程中所起作用的力。特别是，PI 计划研究泡利原理在有组织行为的创建和稳定中的作用。 实验学家在实验室中制作了超冷费米子的受控系统，该系统表现出普遍的集体特性。该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。 使用群论技术获得一阶解析简正模态解的多体摄动方法，PI 计划研究这些简正模态特征的演变，并监测最近测量的属性，包括作为系统参数的激励频率和热力学量接近众所周知支持集体行为的单一政权。这项工作可以提高我们生产和控制这些系统的能力，并增强它们在技术中的使用。该奖项反映了 NSF 的法定使命，并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，被认为值得支持。

项目成果

Analytic-normal-mode frequencies for N identical particles: The microscopic dynamics underlying the emergence and stability of excitation gaps from BCS to unitarity

N 个相同粒子的解析简正模频率：从 BCS 到幺正性激发间隙的出现和稳定性的微观动力学

• DOI: 10.1103/physreva.104.033320
• 发表时间: 2021
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: Watson, D. K.

Exploring the Transition from BCS to Unitarity Using Normal Modes: Energies, Entropies, Critical Temperatures and Excitation Frequencies

• DOI: 10.1007/s10909-023-02966-2
• 发表时间: 2023-05
• 期刊: Journal of Low Temperature Physics
• 影响因子: 2
• 作者: D. K. Watson