The wavefunction is the complex distribution used to completely describe a quantum system, and is central to quantum theory. But despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition. Rather, physicists come to a working understanding of the wavefunction through its use to calculate measurement outcome probabilities by way of the Born rule. At present, the wavefunction is determined through tomographic methods, which estimate the wavefunction most consistent with a diverse collection of measurements. The indirectness of these methods compounds the problem of defining the wavefunction. Here we show that the wavefunction can be measured directly by the sequential measurement of two complementary variables of the system. The crux of our method is that the first measurement is performed in a gentle way through weak measurement, so as not to invalidate the second. The result is that the real and imaginary components of the wavefunction appear directly on our measurement apparatus. We give an experimental example by directly measuring the transverse spatial wavefunction of a single photon, a task not previously realized by any method. We show that the concept is universal, being applicable to other degrees of freedom of the photon, such as polarization or frequency, and to other quantum systems--for example, electron spins, SQUIDs (superconducting quantum interference devices) and trapped ions. Consequently, this method gives the wavefunction a straightforward and general definition in terms of a specific set of experimental operations. We expect it to expand the range of quantum systems that can be characterized and to initiate new avenues in fundamental quantum theory.

We present a method for measuring the transverse electric field profile of a beam of light which allows for direct phase retrieval. The measured values correspond, within a normalization constant, to the real and imaginary parts of the electric field in a plane normal to the direction of propagation. This technique represents a self-referencing method for probing the wavefront characteristics of light.

Characterizing point defects that produce deep states in nanostructures is imperative when designing next-generation electronic and optoelectronic devices. Light emission and carrier transport properties are strongly influenced by the energy position and concentration of such states. The primary objective of this work is to fingerprint the electronic structure by characterizing the deep levels using a combined optical and electronic characterization, considering ZnSe nanowires as an example. Specifically, we use low temperature photoluminescence spectroscopy to identify the dominant recombination mechanisms and determine the total defect concentration. The carrier concentration and mobility are then calculated from electron transport measurements using single nanowire field effect transistors, and the measured experimental data were used to construct a model describing the types, energies, and ionized fraction of defects and calculate the deviation from stoichiometry. This metrology is hence demonstrated to provide an unambiguous means to determine a material’s electronic structure.

We analyze a novel antenna effect that resonantly enhances the photocurrent response of end-contacted P-i-N junction nanowire gratings, due to coupling of incident radiation into the grating's multiple-scattering electromagnetic modes. Quantitative characterization of these resonances was performed by spectral and polarization-resolved photocurrent measurements on gratings with N = 500, 200 and 100 nanowires, aided by electron beaminduced current measurements, and in excellent agreement with electromagnetic scattering theory. Despite the small scattering cross-section of each nanowire, with triangular cross-section (height 8 nm, width 6 nm), the measured quality 6

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