Number-Theory-Inspired Effects in Cold Atoms

冷原子中受数论启发的效应

• 批准号: 2309271
• 负责人: Maxim Olchanyi
• 金额: $ 21.24万
• 依托单位: University of Massachusetts Boston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-15 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2309271&HistoricalAwards=false
• 关键词: Number; Theory; Inspired; Effects; Cold

Recent experimental advances in creating tailored traps for individual atoms have allowed for complete control of the quantum energy levels in those traps. One of the potential applications of these techniques is "experimental number theory". In such applications, the physical effects of a quantum system are engineered based on the validity of a particular conjecture or a particular theorem of the number theory. Under this grant, the PI will address a mathematical identity that is related to sums of squares of integers and also a mathematical conjecture which states that any even number is a sum of two prime numbers. In both cases, an appearance of previously unknown physical effects is foreseen, such as a new example of a violation of the quantum-classical correspondence. Broader impacts of the project include collaboration with the DoD STARBASE Academy youth outreach program at the Hanscom Air Force Base and the development of an educational program which introduces five out of the nine NSF Key Concepts for Future QIS Learners, aimed at Title I school districts in northeastern Massachusetts. The following quantum systems relevant to the number theory are addressed. (a) A potential whose one-particle spectrum is the logarithms of all natural numbers. This potential is expected to demonstrate a resonant transition cascade, absent in its classical counterpart. Population dynamics in a resonant cascade will be sensitive to the properties of the prime factorization of the energy levels involved. (b) A potential whose one particle spectrum is given by the logarithms of sums of two squares of the naturals. This set also supports resonant cascades via the so-called Diophantus-Brahmagupta–Fibonacci identity. (c) Two weakly interacting atoms in an external potential whose spectrum is the primes, plus a small periodic perturbation whose frequency is 2. The existence of a resonant cascade in this system is predicated on the validity of Goldbach’s conjecture, which is famously still unproven.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.

最近在为单个原子创建定制陷阱方面取得的实验进展已经允许完全控制这些陷阱中的量子能级，这些技术的潜在应用之一是“实验数论”，在此类应用中，量子系统的物理效应。是基于数论的特定猜想或特定定理的有效性而设计的。在这项资助下，PI 将解决与整数平方和相关的数学恒等式以及指出任何偶数的数学猜想。是在这两种情况下，都会出现以前未知的物理效应，例如违反量子经典对应关系的新例子，该项目的更广泛影响包括与国防部星基学院青年外展的合作。汉斯科姆空军基地的计划和教育计划的开发，介绍了 NSF 未来 QIS 学习者的九个关键概念中的五个，针对马萨诸塞州东北部的第一章学区。讨论了以下与数论相关的量子系统。 。 (a) 一种势，其单粒子谱是所有自然数的对数，该势预计将展示共振级联中的共振跃迁级联，而共振级联中的群体动力学将对素数的性质敏感。 (b) 其一个粒子谱由两个自然数平方和的对数给出的势。 (c) 外部势中两个弱相互作用的原子，其频谱为素数，加上频率为 2 的小周期性扰动。该系统中共振级联的存在取决于哥德巴赫的有效性。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。