一种推广的含时Jaynes-Cummings模型中的几何相因子

Geometric phase factors in a generalized time-dependent Jaynes-Cummings model

利用Lewis-Riesenfeld不变量理论,研究了一种推广的含时Jaynes-Cummings模型中的动力学相因子和几何相因子。发现在循环条件下,系统中的几何相因子与电磁场的频率、原子和场的耦合系数、原子能级差均无关。这表明几何相因子具有纯几何特征和拓扑特征,表示厄米线丛上的和乐。

By using the Lewis-Riesenfeld invariant theory, we study the dynamical and geometric phases factors in a generalized time-dependent Jaynes-Cummings model. It is found that the geometric phases factor in a cycle case have nothing to do with the frequency of the electromagnetic wave, the coupling strength between the atom and the light field, and the energy difference between two levels of the atom. It is apparent that the geometric phase factors have pure geometric and topological characteristics, which shows that they represent the holonomy in the Hermitian linear bundle.