Quantum Phase Extraction in Isospectral Electronic Nanostructures
Abstract
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.
Cite
@article{arxiv.0803.2328,
title = {Quantum Phase Extraction in Isospectral Electronic Nanostructures},
author = {Christopher R. Moon and Laila S. Mattos and Brian K. Foster and Gabriel Zeltzer and Wonhee Ko and Hari C. Manoharan},
journal= {arXiv preprint arXiv:0803.2328},
year = {2008}
}
Comments
Published 8 February 2008 in Science; 13 page manuscript (including 4 figures) + 13 page supplement (including 6 figures); supplementary movies available at http://mota.stanford.edu