Universality and Beyond in Atoms with Large Scattering Lengths

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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.