论文标题
根据Bloch球的riemannian几何形状的三脚架原子系统中绝热通道的研究
Study of the adiabatic passage in tripod atomic systems in terms of the Riemannian geometry of the Bloch sphere
论文作者
论文摘要
我们基于差异几何形状的方法对受刺激的拉曼绝热通道过程进行了分析。目前的作品灵感来自Bruce W. Shore等人的出色文章。 （R. G. Unanyan，B。W。Shore和K. BergmannPhys。Rev.A \ Textbf {59}，2910（1999））。我们演示了量子三脚架系统中绝热通道的纯几何解释是如何作为黑暗状态矢量沿Bloch球的Riemannian平行传输的，可以描述给定的Stokes，泵和控制激光激发脉冲的系统的演变。结合Dykhne-Davis-Pechukas绝热标准和球圆的最小原理，该方法允许获得高富达三脚架分数搅拌的最佳激光脉冲序列的分析形式。与$λ$ - 系统中的常规搅拌相反，最佳激光脉冲序列的高斯近似值允许在没有明显的振动性或其他对人口转移准确性的不存在的振动性或其他有害的效果的情况下达到$ 10^{ - 7} $的不忠$ 10^{ - 7} $。
We present an analysis of the stimulated Raman adiabatic passage processes based on the methods of differential geometry. The present work was inspired by an excellent article by Bruce W. Shore et al. (R. G. Unanyan, B. W. Shore, and K. Bergmann Phys. Rev. A \textbf{59}, 2910 (1999)). We demonstrate how a purely geometric interpretation of the adiabatic passage in quantum tripod systems as a Riemannian parallel transport of the dark state vector along the Bloch sphere allows describing the evolution of the system for a given sequence of Stokes, pump and control laser excitation pulses. In combination with the Dykhne-Davis-Pechukas adiabaticity criterion and the minimax principle for circles on a sphere, this approach allows obtaining the analytical form of the optimal laser pulse sequences for a high fidelity tripod fractional STIRAP. In contrast to the conventional STIRAP in $Λ$-systems, the Gaussian approximations of the optimal laser pulse sequences allow reaching the infidelity of $10^{-7}$ for the adiabaticity parameter of $300$ without noticeable oscillatory or other detrimental effects on population transfer accuracy.
