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