Moon Christopher R, Mattos Laila S, Foster Brian K, Zeltzer Gabriel, Ko Wonhee, Manoharan Hari C
Department of Physics, Stanford University, Stanford, CA 94305, USA.
Science. 2008 Feb 8;319(5864):782-7. doi: 10.1126/science.1151490.
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.
量子相位不能直接观测到，通常由干涉测量方法来确定。我们提出了一种从测量的单态概率密度映射完整电子波函数（包括内部量子相位信息）的方法。我们利用了具有不同形状但相同共振的鼓状流形这一数学发现，并构建了具有匹配电子结构但物理结构不同的量子等谱纳米结构。对这些“量子鼓”（由单独定位的一氧化碳分子限制在铜（111）表面上的简并二维电子态）进行量子测量（扫描隧道显微镜）表明，等谱性提供了一个额外的拓扑自由度，能够实现稳健的量子态移植和相位提取。
