Quantum Phase Extraction in Isospectral Electronic Nanostructures

Details Quantum Phase Extraction in Isospectral Electronic Nanostructures Quantum Phase Extraction in Isospectral Electronic Nanostructures

2008-03-16

arxiv.org/abs/0803.2328v1

Science 319, 782-787 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Published 8 February 2008 in Science; 13 page manuscript (including 4 figures) + 13 page supplement (including 6 figures); sup

Scientific paper

10.1126/science.1151490

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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