The concept of geometric phase acquired by a quantum state during its evolution is generalized to the subspace of states of evolving quantum system. Physical motivation of this generalization comes from the effect of coherent population trapping. Under certain conditions, there exists a two-dimensional “dark” subspace of atomic ground states that does not interact with the external radiation. The structure of this “dark” subspace depends on the local field amplitude. We show that certain mathematical difficulties in finding the geometric phase for “dark” subspaces can be circumvented with the help of the orthogonal “bright” subspace.

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相干种群捕获中“暗”子空间的几何相位

将一个量子态在演化过程中获得的几何相位的概念推广到演化量子系统的状态子空间。这种概括的物理动机来自一致的人口诱捕效应。在某些条件下，存在一个不与外部辐射相互作用的原子基态的二维“暗”子空间。这个“暗”子空间的结构取决于局部场幅度。我们表明，在正交“亮”子空间的帮助下，可以规避为“暗”子空间寻找几何相位的某些数学困难。