Universality and Beyond in Atoms with Large Scattering Lengths

科学上的还原论概念是指在最小长度尺度上系统的物理特性往往决定宏观性质和现象的一般观察。所以铜线和铝线的表现不同是因为组成它们的原子的物理特性不同。对还原论的背离很少，但确实存在。这个项目探索了被称为“普遍性”的还原论的分解，这种分解有时会在超冷原子的集合中表现出来。超冷原子的集合为宇宙现象提供了特别重要的例子，因为它们可以被精确地控制和探测。它们还为其他物理领域的普遍性提供了有价值的范例，包括核物理和粒子物理、天体物理学和凝聚态物理。在稀薄的超冷气体中观察到的普遍性质的例子，与所使用的原子种类无关，包括弱束缚团簇的束缚能，原子和团簇之间碰撞的反应速率，以及被困系综的稳定性或寿命。这个项目将有助于解释这些结果，并预测超冷系统的其他可观察的、普遍的特性。本研究项目的目标是扩展我们对由原子组成的少体和多体系统的普遍方面的理解，这些原子的散射长度比它们相互作用的范围大。该项目有三大重点：(1)最近在计算费什巴赫共振附近振荡磁场的跃迁速率方面取得了突破，将应用于费米子原子超流体中成对费米子的分裂。其目的是为首次直接测量超流体的配对间隙的实验提供动力。(2)近年来首次进行了由具有无限大散射长度的玻色子原子组成的单一玻色气体的实验。将开发一种新的理论方法来研究统一玻色气体，该方法是基于在空间维度（即3）中使用围绕临界维度2和4的展开进行插值，在这些维度上问题更简单。(3)最简单的普遍性质对应于原子间势的范围取为零，其强度取为无穷大而散射长度固定的数学极限。可以通过扩大范围的幂来确定其他的普遍方面。最近简化玻色子原子一阶范围修正的工作将被扩展并应用于冷原子实验的结果。

The concept of reductionism in science refers to the general observation that physical characteristics of systems at the smallest length scale often determine macroscopic properties and phenomena. So copper wires and aluminum wires behave differently because of the physical characteristics of the atoms of which they are composed. Departures from reductionism are rare, but they do exist. This project explores a breakdown of reductionism known as "universality" that is sometimes displayed by ensembles of ultra-cold atoms. Ensembles of ultra-cold atoms provide especially important examples of universal phenomena because they can be controlled and probed with exquisite precision. They also provide valuable paradigms for universality in other fields of physics, including nuclear and particle physics, astrophysics, and condensed-matter physics. Examples of the universal properties observed in dilute, ultra-cold gases, independent of the species of atom employed, include the binding energies of weakly bound clusters, the reaction rates for collisions between atoms and clusters, and the stability or lifetime of trapped ensembles. This project will help to interpret these results, and to predict other observable, universal properties of ultra-cold systems. The goal of this research project is to extend our understanding of universal aspects of few-body and many-body systems consisting of atoms whose scattering length is large compared to the range of their interactions. The project has three major thrusts: (1) A recent breakthrough in calculating transition rates from an oscillating magnetic field near a Feshbach resonance will be applied to the breakup of paired fermions in a superfluid of fermionic atoms. The goal is to provide motivation for experiments that would make the first direct measurements of the pairing gap for superfluidity. (2) The first experiments on the unitary Bose gas, which consists of bosonic atoms with infinitely large scattering length, were carried out in the last few years. A new theoretical approach to the unitary Bose gas will be developed based on interpolating in the dimension of space (which is 3) using expansions around the critical dimensions 2 and 4, where the problem is simpler. (3) The simplest universal properties correspond to the mathematical limit in which the range of the interatomic potential is taken to zero and its strength is taken to infinity with the scattering length fixed. Additional universal aspects can be identified by expanding in powers of the range. Recent work simplifying the first-order range corrections for bosonic atoms will be extended and applied to results from cold atom experiments.