Quantum phase extraction in isospectral electronic nanostructures.
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.
Moon
Christopher R
CR
Department of Physics, Stanford University, Stanford, CA 94305, USA.
Mattos
Laila S
LS
Foster
Brian K
BK
Zeltzer
Gabriel
G
Ko
Wonhee
W
Manoharan
Hari C
HC