2008/02/07 by Christopher R. Moon, Laila Mattos, Laila S. Mattos +5
Engineering · Physics and Astronomy · #Molecular Junctions and Nanostructures #Quantum and electron transport phenomena #Spectroscopy and Quantum Chemical Studies #cond-mat.mes-hall #cond-mat.mtrl-sci #quant-ph
paper · pdf · doi:10.1126/science.1151490
published as Science 319, 782-787 (2008) · 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
openalex publication_date 2008/02/07 · arxiv created 2008/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Quantum phase is not directly 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 with matching electronic structure but divergent physical structure. Quantum measurement (scanning tunneling microscopy) of these "quantum drums"-degenerate two-dimensional electron states on the copper(111) surface confined by individually positioned carbon monoxide molecules-reveals that isospectrality provides an extra topological degree of freedom enabling robust quantum state transplantation and phase extraction.