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.

We address quantum invisibility in the context of electronics in nanoscale quantum structures. In analogy with metamaterials, we use the freedom of design that quantum corrals provide and show that quantum mechanical objects can be hidden inside the corral, with respect to inelastic electron scattering spectroscopy in combination with scanning tunneling microscopy, and we propose a design strategy. A simple illustration of the invisibility is given in terms of an elliptic quantum corral containing a molecule, with a local vibrational mode, at one of the foci. Our work has implications to quantum information technology and presents new tools for nonlocal quantum detection and distinguishing between different molecules.

We describe measurements of spin dynamics in the two-dimensional electron gas in GaAs/GaAlAs quantum wells. Optical techniques, including transient spin-grating spectroscopy, are used to probe the relaxation rates of spin polarization waves in the wavevector range from zero to 6 x 10{sup 4} cm{sup -1}. We find that the spin polarization lifetime is maximal at nonzero wavevector, in contrast with expectation based on ordinary spin diffusion, but in quantitative agreement with recent theories that treat diffusion in the presence of spin-orbit coupling.

The ultimate miniaturization of electronic devices will likely require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric interpretation: this state space - or Hilbert space - is spanned by mutually orthogonal state vectors corresponding to the quantized degrees of freedom of the real-space system. Measurement of superpositions is akin to accessing the direction of a vector in Hilbert space, determining an angle of rotation equivalent to quantum phase. Here we show that an individual atom inside a designed quantum corral1 can control this angle, producing arbitrary coherent superpositions of spatial quantum states. Using scanning tunnelling microscopy and nanostructures assembled atom-by-atom we demonstrate how single spins and quantum mirages can be harnessed to image the superposition of two electronic states. We also present a straightforward method to determine the atom path enacting phase rotations between any desired state vectors. A single atom thus becomes a real-space handle for an abstract Hilbert space, providing a simple technique for coherent quantum state manipulation at the spatial limit of condensed matter.

In this perspective, we take a critical look at the research progress within the nanowire community for the past decade. We discuss issues on the discovery of fundamentally new phenomena versus performance benchmarking for many of the nanowire applications. We also notice that both the bottom-up and top-down approaches have played important roles in advancing our fundamental understanding of this new class of nanostructures. Finally we attempt to look into the future and offer our personal opinions on what the future trends will be in nanowire research.

The authors study the reaction e{sup +}e{sup -} {yields} e{sup +}e{sup -} {eta}{sub c}, {eta}{sub c} {yields} K{sub S}K{sup {+-}}{pi}{sup {-+}} and obtain {eta}{sub c} mass and width values 2982.2 {+-} 0.4 {+-} 1.6 MeV/c{sup 2} and 31.7 {+-} 1.2 {+-} 0.8 MeV, respectively. They find {Lambda}({eta}{sub c} {yields} {gamma}{gamma}){Beta}({eta}{sub c} {yields} K{bar K}{pi}) = 0.374 {+-} 0.009 {+-} 0.031 keV, and measure the {gamma}{gamma}* {yields} {eta}{sub c} transition form factor in the momentum transfer range from 2 to 50 GeV{sup 2}. The analysis is based on 469 fb{sup -1} of integrated luminosity collected at PEP-II with the BABAR detector at e{sup +}e{sup -} center-of-mass energies near 10.6 GeV.