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Quantum Phase Extraction in Isospectral Electronic Nanostructures
The phase of a wave function collapses when measurements are made, so additional information is needed to determine phase, and several methods have been developed based on interference with reference waves. Moon et al. describe a non-interferometric approach to phase-determination based on the isospectrality, which describes pairs of simple polygonal shapes that have the same frequency response--that is, if these shapes were drumheads, they could sound the same and be indistinguishable. The authors used scanning tunneling microscopy to position CO molecules on the Cu(111) surface at cryogenic temperatures to bound isospectral shapes. Despite the imperfect nature of this boundary, the spectral fingerprints of the two-dimensional electronic states in the terahertz range were the same within experimental error. The authors then used this property to extract the wave function phase. Phase extraction should be possible in two-dimensional quantum systems provided that the boundary shapes can be constructed.

Science 8 February 2008:
Vol. 319. no. 5864, pp. 782 - 787
DOI: 10.1126/science.1151490
Last update on 2008-02-08