dorsal/arxiv
View SchemaMeasurement Induced Localization of Relative Degrees of Freedom
| Authors | Hugo Cable, Peter L. Knight, Terry Rudolph |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411167 |
| URL | https://arxiv.org/abs/quant-ph/0411167 |
| DOI | 10.1103/PhysRevA.71.042107 |
| Journal | Phys. Rev. A 71, 042107 (2005) |
Abstract
We present a comprehensive study, using both analytical and numerical methods, of measurement-induced localization of relational degrees of freedom. Looking first at the interference of two optical modes, we find that the localization of the relative phase can be as good for mixed states - in particular for two initially Poissonian or thermal states - as for the well-known case of two Fock states. In a realistic setup the localization for mixed states is robust and experimentally accessible, and we discuss applications to superselection rules. For an ideal setup and initial Fock states we show how a relational Schr\"{o}dinger cat state emerges, and investigate circumstances under which such a state is destroyed. In our second example we consider the localization of relative atomic phase between two Bose Einstein condensates, looking particularly at the build up of spatial interference patterns, an area which has attracted much attention since the work of Javanainen and Yoo. We show that the relative phase localizes much faster than was intimated in previous studies focusing on the emerging interference pattern itself. Finally, we explore the localization of relative spatial parameters discussed in recent work by Rau, Dunningham and Burnett. We retain their models of indistinguishable scattering but make different assumptions. In particular we consider the case of a real distant observer monitoring light scattering off two particles, who records events only from a narrow field of view. The localization is only partial regardless of the number of observations. This paper contributes to the wider debate on relationism in quantum mechanics, which treats fundamental concepts - reference frames and conservation laws - from a fully quantum and operational perspective.
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"abstract": "We present a comprehensive study, using both analytical and numerical\nmethods, of measurement-induced localization of relational degrees of freedom.\nLooking first at the interference of two optical modes, we find that the\nlocalization of the relative phase can be as good for mixed states - in\nparticular for two initially Poissonian or thermal states - as for the\nwell-known case of two Fock states. In a realistic setup the localization for\nmixed states is robust and experimentally accessible, and we discuss\napplications to superselection rules. For an ideal setup and initial Fock\nstates we show how a relational Schr\\\"{o}dinger cat state emerges, and\ninvestigate circumstances under which such a state is destroyed. In our second\nexample we consider the localization of relative atomic phase between two Bose\nEinstein condensates, looking particularly at the build up of spatial\ninterference patterns, an area which has attracted much attention since the\nwork of Javanainen and Yoo. We show that the relative phase localizes much\nfaster than was intimated in previous studies focusing on the emerging\ninterference pattern itself. Finally, we explore the localization of relative\nspatial parameters discussed in recent work by Rau, Dunningham and Burnett. We\nretain their models of indistinguishable scattering but make different\nassumptions. In particular we consider the case of a real distant observer\nmonitoring light scattering off two particles, who records events only from a\nnarrow field of view. The localization is only partial regardless of the number\nof observations. This paper contributes to the wider debate on relationism in\nquantum mechanics, which treats fundamental concepts - reference frames and\nconservation laws - from a fully quantum and operational perspective.",
"arxiv_id": "quant-ph/0411167",
"authors": [
"Hugo Cable",
"Peter L. Knight",
"Terry Rudolph"
],
"categories": [
"quant-ph",
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],
"doi": "10.1103/PhysRevA.71.042107",
"journal_ref": "Phys. Rev. A 71, 042107 (2005)",
"title": "Measurement Induced Localization of Relative Degrees of Freedom",
"url": "https://arxiv.org/abs/quant-ph/0411167"
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