dorsal/arxiv
View SchemaManifestations of quantum holonomy in interferometry
| Authors | Erik Sjöqvist, David Kult, Johan Åberg |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0607198 |
| URL | https://arxiv.org/abs/quant-ph/0607198 |
| DOI | 10.1103/PhysRevA.74.062101 |
| Journal | Phys. Rev. A 74, 062101 (2006) |
Abstract
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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"abstract": "Abelian and non-Abelian geometric phases, known as quantum holonomies, have\nattracted considerable attention in the past. Here, we show that it is possible\nto associate nonequivalent holonomies to discrete sequences of subspaces in a\nHilbert space. We consider two such holonomies that arise naturally in\ninterferometer settings. For sequences approximating smooth paths in the base\n(Grassmann) manifold, these holonomies both approach the standard holonomy. In\nthe one-dimensional case the two types of holonomies are Abelian and coincide\nwith Pancharatnam\u0027s geometric phase factor. The theory is illustrated with a\nmodel example of projective measurements involving angular momentum coherent\nstates.",
"arxiv_id": "quant-ph/0607198",
"authors": [
"Erik Sj\u00f6qvist",
"David Kult",
"Johan \u00c5berg"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.062101",
"journal_ref": "Phys. Rev. A 74, 062101 (2006)",
"title": "Manifestations of quantum holonomy in interferometry",
"url": "https://arxiv.org/abs/quant-ph/0607198"
},
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