新型费米原子气体中相互作用效应的理论研究

项目名称： 新型费米原子气体中相互作用效应的理论研究

项目编号： No.11204152

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 物理学I

项目作者： 俞振华

作者单位： 清华大学

项目金额： 24万元

中文摘要： 近期实验已在制备具有自旋轨道耦合及束缚于二维空间的费米原子气体方面取得重大突破。这些进展触发我们研究原子间的相互作用在这两类新型费米气体中的效应。BEC-BCS crossover的研究表明原子间的近程关联具有确定的形式。由近程关联定义的接触关联强度（contact）更与体系的热力学函数，自旋关联等有直接联系。我们将研究自旋轨道耦合对费米原子间近程关联的定性及定量影响：考察自旋轨道耦合的引入是否会改变关联在近程的渐近形式；计算关联强度对自旋轨道耦合强度的定量依赖。对于二维费米原子气体，原子间的相互作用引发量子反常，使得体系的标度不变性被破坏。我们将研究标度不变性的破坏对束缚于谐振子势中的二维费米原子气体呼吸模的影响。我们将计算由相互作用产生的呼吸模频率的偏移。我们还将使用接触关联强度作为量子反常的定量表征，研究温度对二维费米原子气体的量子反常的影响。

中文关键词： p波接触关联；超辐射；窄Feshbach共振；超Efimov态；

英文摘要： Recent experiments have made important breakthrough in realizing ultracold atomic Fermi gases with spin-orbit coupling or confined in two dimensional spaces. Such advances stimulate us to study the effects of the interatomic interactions in these two novel Fermi gases. The study of the BEC-BCS problem manifests that the inter-atom correlations at short distances have a fixed asymptotic form. The correlation strength (contact), defined via the asymptotic form, has direct relations with thermodynamic functions and spin-correlations. We will study the qualitative and quantitative effects of the spin-orbit coupling on the short-range correlations: investigate whether the introduction of the spin-orbit coupling would change the asymptotic form of the short-range correlations; calculate the quantitative dependence of the correlation strength on the magnitude of the spin-orbit coupling. For two dimensional atomic Fermi gases, interatomic interactions give rise to quantum anomaly, breaking down the scale invariance of the system. We will study the effects of the breaking of the scale invariance on the breathing mode of the two dimensional atomic Fermi gases trapped in harmonic potentials. We will calculate the frequency shift of the breathing mode due to the interactions. We will also use the correlation strength as a m

英文关键词： p-wave contacts；superradiance；narrow Feshbach resonance；super Efimov states；