【作者】 邓敏；

【导师】 吕嵘；

【作者基本信息】 清华大学 ， 物理学， 2018， 博士

【摘要】 高波教授在1998年得到了范德瓦尔斯势-C₆ r⁶的解析解后,建立起了中性冷原子碰撞的量子亏损理论。该理论只需少量参数就可以解析描述任意分波的低能散射行为和共振态附近的相互作用,因此极大的方便了我们理解和处理冷原子系统中的高分波相互作用。本文始终围绕量子亏损理论来处理冷原子物理中的超冷碰撞问题,包括超冷原子玻色爱因斯坦凝聚体中的偶极自旋翻转损耗过程,零能阈值附近的Feshbach共振和形状共振的特征行为。本文首先利用单通道量子亏损理论来研究玻色原子⁸⁷Rb凝聚体中的非弹性偶极弛豫过程。实验发现偶极-偶极相互作用造成的原子损耗率随磁场关系存在低“谷”和高“峰”的独特线型结构。量子亏损理论给出的计算结果很好的解释了这种独特的线型,并和多通道耦合方程数值计算结果基本一致。而采用玻恩近似和扭曲波玻恩近似无法完全解释这些实验结果,其原因在于量子亏损理论可以准确的描述范德瓦尔斯半径区域的散射过程。随后,我们把多通道量子亏损理论应用到异核原子超冷混合物(⁸⁵Rb和⁸⁷Rb原子)和超冷原子⁴¹K这两个体系中。该理论可以预测超冷碰撞中的磁Feshbach共振和形状共振位置,判断其宽窄性质,并可有效描述共振附近的相互作用。根据理论计算的结果,在⁸⁵Rb和⁸⁷Rb混合物实验中发现了p波和d的宽共振,它们的原子损耗峰上出现了特征的双劈裂和三劈裂结构。我们发展了一种多通道量子亏损理论和Kohn变分法相结合的方法,用来理解观察到的劈裂结果。另外,理论计算还表明:在零能共振的阈值附近,“窄”共振态的位置,寿命和散射相移都和“宽”共振有明显区别,它们随能量有比较强烈的变化,背景共振态或者背景束缚态也会对共振态阈值附近的行为产生较大影响。在“宽”的共振峰附近,我们还研究了两分量BEC混合物在存在p波相互作用时的稳态相图。研究表明正的p波相互作用强度有利于增强混合,而当囚禁两分量BEC的谐振子势场不同时,保持了空间旋转不变性的分离相也可以是系统稳定的基态。同时,文中还给出了d波相互作用的具体形式。更多还原

【Abstract】 Prof.Bo Gao obtained the analytical solution of the Van der Waals potential-C₆ r⁶ in 1998 which established the foundation for a semi-analytical quantum-defect theory（QDT）for cold neutral atom collisions.This theory can analytically describe the low-energy scattering behavior for an arbitrary partial wave and the atomic interactions around a resonance with a few parameters.It greatly facilitates our understanding of high partial wave interactions in cold atomic physics.This thesis employs the quantum-defect theory to study several ultracold collision problems in cold-atom physics,including inelastic dipolar relaxation of spinor Bose Einstein condensates（BECs）,the characteristic behavior of the Feshbach resonance and shape resonance around a zero energy threshold.Concerning the dipolar relaxation of atomic spinor condensates,high precision experimental observations in our group reveal that the atomic loss rate caused by dipole-dipole interactions exhibits a unique linear structure with a“dip”and“peak”in the magnetic field dependence.The QDT well explains such a unique line shape and is consistent with the numerical results from the multi-channel coupled equations.The reason attributed to the accurate description of the scattering process between alkali-metal atoms beyond the Van der Waals radius region.We also apply the multi-channel quantum-defect theory（MQDT）to two specific atomic interactions,between a ⁸⁷Rb atom and a ⁸⁵Rb atom,and between two ⁴¹K atoms.The QDT theory allows for the prediction of magnetic Feshbach resonance and shape resonance positions,determine their classification into being“broad”and“narrow”resonances,and describes their effective interactions near resonances.Following such theoretical guidances,the“broad”resonances of p-wave and d-wave characters have been found experimentally,and their atomic loss spectroscopies show a corresponding doublet and triplet splitting structures.An improved dipolar loss theory is developed for the understanding of these multiplet structures in terms of a few parameters based on the MQDT and the Kohn variational principle.Its applications to the non-zero partial wave interspecies broad Feshbach resonances（p-wave and d-wave）as observed in the mixtures of ⁸⁵Rb and ⁸⁵Rb atoms will be compared to and be reported.In addition,the theoretical calculations also show that near the threshold of zero-energy resonance,the position,lifetime and scattering phase shift of a“narrow”resonance state are distinctly different from those of“broad”resonances,and they are sensitive to the the change of magnetic field.In addition,a background resonance state or a background bound state also exhibit a great influence on the threshold behavior of a resonance.In the vicinity of a“broad”resonance,we study the steady-state phase diagrams of a two-component BEC mixtures in the presence of an interspecies p-wave interaction.Our numerical calculations reveal positive p-wave interactions between BEC mixtures would enhance their miscibility,and when the condensates for the two species experience different harmonic trap potentials,a spatial not completely overlaped phase that maintains spatial rotation invariance can corresponds to the stable ground state of the system.Finally,an explicit form of the pseudo-potential for d-wave interaction is presented as well.更多还原