基于量子亏损理论的超冷原子分子碰撞研究
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摘要
本学位论文采用量子亏损理论研究了超冷原子-原子、超冷分子-分子之间的碰撞过程以及材料表面对入射超冷原子的量子反射,主要工作包括以下三个方面：
(1)发展了利用解析量子亏损矩阵计算超冷原子碰撞的理论方法。该理论计算方法不依赖精确的电子相互作用势能曲线,只需要知道碰撞原子对的长程范德瓦尔斯系数、单/三重态散射长度,在不求解多通道耦合方程的情况下,可以给出碰撞原子对的散射性质和相应的双原子分子弱束缚能级。我们计算了6Li-40K碰撞体系Feshbach共振位置,理论计算结果与实验观测值符合得很好。
(2)利用量子亏损理论研究了超冷极性分子在外电场中的放热反应碰撞。通过引入两组参数Dc3和Dent,给出了分子间相互作用势对入射波函数的反射、透射幅度的表达式。借助于反射波、透射波等概念,我们建立了一个清晰的碰撞动力学物理图像。当短程反应几率等于1时,描述分子从入射通道跃迁到产物通道的幅度等于入射波函数中穿过长程区间的部分。当短程反应几率小于1时,跃迁幅度可以看作由长程和短程势反射的波函数的相干叠加,反应速率随电场变化曲线中的共振结构由跃迁幅度的相干增强和相干减弱形成。
(3)建立了描述材料表面反射超冷原子的三参数量子反射理论模型。基于量子亏损理论,我们定义了三个不随能量变化的参数,原子与表面在非阻滞区相互作用势的信息都包含在这三个参数中。我们计算了导体表面对钠原子的量子反射。结果表明,在量子反射现象明显的能量范围内,三参数模型可以给出精确的量子反射幅度。另外,我们建立的量子反射理论模型便于拟合实验数据,从中提取原子与表面相互作用势的相关信息。
This dissertation develops theoretical models for ultracold atomic and molecular collisions in external fields based on quantum defect theory. The main works are summarized as follows.
(1)We present a theoretical model for describing ultracold atomic collision based on the multichannel quantum defect theory. An analytical expression for the quantum-defect ma-trix Y is derived for the truncated1/R6model potential, and the threshold behaviors of the quantum-defect parameters are discussed. The model allows us to predict the Feshbach resonances when the singlet and triplet scattering lengths are known, or fit the scattering lengths when a couple of Feshbach resonances is located experimentally. As an illustrative example, we investigate the6Li-40K scattering. The theoretical results agree quite well with the experimental values.
(2)We investigate the scattering dynamics governed by the long-range van der Waals plus dipole-dipole interaction potential,-C6/R6-C3/R3, which describes the long-range interaction between two polar molecules in an electric field. In the spirit of quantum defect theory, a set of parameters which are nearly constants in the threshold regime is defined to characterize the scattering process. Using appropriate boundary conditions for the scattering wave functions and relevant parameters, we explore the quantum reflection by and quantum tunneling through the long-range potential. As a sample application, the reactive collision rates of40K87Rb+40K87Rb are calculated.
(3)We investigate the quantum reflection by the Casimir-Polder potential which scales as-1/r3at short separation and as-1/r4at long separation. Using the available analytical solutions for the-1/r4potential and quantum defect theory, we develop a three-parameter model for quantum reflection. The three parameters characterizing the potential are es-sentially constant near the threshold. The application scope of the model is examined. For potential dominated by the-1/r4behaviour, which is the case in many realistic atom-surface systems, our model gives accurate results over the energy range in which the quantum re-flection is significant. Moreover, this parameterized model allows one to fit the experimental data efficiently.
(1)发展了利用解析量子亏损矩阵计算超冷原子碰撞的理论方法。该理论计算方法不依赖精确的电子相互作用势能曲线,只需要知道碰撞原子对的长程范德瓦尔斯系数、单/三重态散射长度,在不求解多通道耦合方程的情况下,可以给出碰撞原子对的散射性质和相应的双原子分子弱束缚能级。我们计算了6Li-40K碰撞体系Feshbach共振位置,理论计算结果与实验观测值符合得很好。
(2)利用量子亏损理论研究了超冷极性分子在外电场中的放热反应碰撞。通过引入两组参数Dc3和Dent,给出了分子间相互作用势对入射波函数的反射、透射幅度的表达式。借助于反射波、透射波等概念,我们建立了一个清晰的碰撞动力学物理图像。当短程反应几率等于1时,描述分子从入射通道跃迁到产物通道的幅度等于入射波函数中穿过长程区间的部分。当短程反应几率小于1时,跃迁幅度可以看作由长程和短程势反射的波函数的相干叠加,反应速率随电场变化曲线中的共振结构由跃迁幅度的相干增强和相干减弱形成。
(3)建立了描述材料表面反射超冷原子的三参数量子反射理论模型。基于量子亏损理论,我们定义了三个不随能量变化的参数,原子与表面在非阻滞区相互作用势的信息都包含在这三个参数中。我们计算了导体表面对钠原子的量子反射。结果表明,在量子反射现象明显的能量范围内,三参数模型可以给出精确的量子反射幅度。另外,我们建立的量子反射理论模型便于拟合实验数据,从中提取原子与表面相互作用势的相关信息。
This dissertation develops theoretical models for ultracold atomic and molecular collisions in external fields based on quantum defect theory. The main works are summarized as follows.
(1)We present a theoretical model for describing ultracold atomic collision based on the multichannel quantum defect theory. An analytical expression for the quantum-defect ma-trix Y is derived for the truncated1/R6model potential, and the threshold behaviors of the quantum-defect parameters are discussed. The model allows us to predict the Feshbach resonances when the singlet and triplet scattering lengths are known, or fit the scattering lengths when a couple of Feshbach resonances is located experimentally. As an illustrative example, we investigate the6Li-40K scattering. The theoretical results agree quite well with the experimental values.
(2)We investigate the scattering dynamics governed by the long-range van der Waals plus dipole-dipole interaction potential,-C6/R6-C3/R3, which describes the long-range interaction between two polar molecules in an electric field. In the spirit of quantum defect theory, a set of parameters which are nearly constants in the threshold regime is defined to characterize the scattering process. Using appropriate boundary conditions for the scattering wave functions and relevant parameters, we explore the quantum reflection by and quantum tunneling through the long-range potential. As a sample application, the reactive collision rates of40K87Rb+40K87Rb are calculated.
(3)We investigate the quantum reflection by the Casimir-Polder potential which scales as-1/r3at short separation and as-1/r4at long separation. Using the available analytical solutions for the-1/r4potential and quantum defect theory, we develop a three-parameter model for quantum reflection. The three parameters characterizing the potential are es-sentially constant near the threshold. The application scope of the model is examined. For potential dominated by the-1/r4behaviour, which is the case in many realistic atom-surface systems, our model gives accurate results over the energy range in which the quantum re-flection is significant. Moreover, this parameterized model allows one to fit the experimental data efficiently.
引文
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