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arXiv · 0803.2328

Quantum Phase Extraction in Isospectral Electronic Nanostructures

Christopher R. Moon·Laila S. Mattos·Brian K. Foster·Gabriel Zeltzer·Wonhee Ko·Hari C. Manoharan
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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.

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Christopher R. Moon, Laila S. Mattos, Brian K. Foster, Gabriel Zeltzer, Wonhee Ko, Hari C. Manoharan. 2008-03-16. Quantum Phase Extraction in Isospectral Electronic Nanostructures. https://doi.org/10.1126/science.1151490

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