Quantum Phase Extraction in Isospectral Electronic Nanostructures

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Quantum phase is not a direct observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability densities. We harness the mathematical discovery of drum-like manifolds bearing different shapes but identical resonances, and construct quantum isospectral nanostructures possessing matching electronic structure but divergent physical structure. Quantum measurement (scanning tunneling microscopy) of these 'quantum drums' [degenerate two-dimensional electron states on the Cu(111) surface confined by individually positioned CO molecules] reveals that isospectrality provides an extra topological degree of freedom enabling robust quantum state transplantation and ... continued below

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Moon, Christopher April 28, 2010.

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Quantum phase is not a direct observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability densities. We harness the mathematical discovery of drum-like manifolds bearing different shapes but identical resonances, and construct quantum isospectral nanostructures possessing matching electronic structure but divergent physical structure. Quantum measurement (scanning tunneling microscopy) of these 'quantum drums' [degenerate two-dimensional electron states on the Cu(111) surface confined by individually positioned CO molecules] reveals that isospectrality provides an extra topological degree of freedom enabling robust quantum state transplantation and phase extraction.

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  • Journal Name: Submitted to Science

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  • Report No.: SLAC-PUB-13992
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 979048
  • Archival Resource Key: ark:/67531/metadc930750

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Office of Scientific & Technical Information Technical Reports

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  • April 28, 2010

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

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  • Feb. 17, 2017, 6:36 p.m.

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Moon, Christopher. Quantum Phase Extraction in Isospectral Electronic Nanostructures, article, April 28, 2010; United States. (digital.library.unt.edu/ark:/67531/metadc930750/: accessed November 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.