Manifestations of quantum holonomy in interferometry

Details Manifestations of quantum holonomy in interferometry Manifestations of quantum holonomy in interferometry

2006-07-27

arxiv.org/abs/quant-ph/0607198v2

Phys. Rev. A 74, 062101 (2006)

Physics

Quantum Physics

Some changes, journal reference added

Scientific paper

10.1103/PhysRevA.74.062101

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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