量子完整性在干涉测量中的表现
Manifestations of quantum holonomy in interferometry
摘要：
阿贝尔和非阿贝尔几何相位，被称为量子完整性，在过去已经引起了相当大的关注。在这里，我们表明，它是可能的关联非等价holonomies的离散序列的子空间在希尔伯特空间。我们考虑两个这样的holonomies自然出现在干涉仪设置。对于基（格拉斯曼）流形上的光滑路径序列，这些完整性都接近标准完整性。在一维情况下，这两种类型的holonomies是阿贝尔和符合潘查拉特南的几何相因子。该理论说明了一个模型的例子，涉及角动量相干态的投影测量。
英文摘要：
Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a Hilbert space. We consider two such holonomies that arise naturally in interferometer settings. For sequences approximating smooth paths in the base (Grassmann) manifold, these holonomies both approach the standard holonomy. In the one-dimensional case the two types of holonomies are Abelian and coincide with Pancharatnam's geometric phase factor. The theory is illustrated with a model example of projective measurements involving angular momentum coherent states.
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