Extracting the Density Profile of an Electronic Wave Function in a Quantum Dot

We use a model of a one-dimensional nanowire quantum dot to demonstrate the feasibility of a scanning probe microscope (SPM) imaging technique that can extract both the energy of an electron state and the amplitude of its wave function using a single instrument. This imaging technique can probe electrons that are buried beneath the surface of a low-dimensional semiconductor structure and provide valuable information for the design of quantum devices. A conducting SPM tip, acting as a movable gate, measures the energy of an electron state using Coulomb blockade spectroscopy. When the tip is close to the nanowire dot, it dents the wave function $\Psi(x)$ of the quantum state, changing the electron's energy by an amount proportional to $\mid\Psi(x)\mid^2$. By recording the change in energy as the SPM tip is moved along the length of the dot, the density profile of the electronic wave function can be found along the length of the quantum dot.Engineering and Applied Science

Sorting photons by radial quantum number

The Laguerre-Gaussian (LG) modes constitute a complete basis set for representing the transverse structure of a {paraxial} photon field in free space. Earlier workers have shown how to construct a device for sorting a photon according to its azimuthal LG mode index, which describes the orbital angular momentum (OAM) carried by the field. In this paper we propose and demonstrate a mode sorter based on the fractional Fourier transform (FRFT) to efficiently decompose the optical field according to its radial profile. We experimentally characterize the performance of our implementation by separating individual radial modes as well as superposition states. The reported scheme can, in principle, achieve unit efficiency and thus can be suitable for applications that involve quantum states of light. This approach can be readily combined with existing OAM mode sorters to provide a complete characterization of the transverse profile of the optical field

Vacuum-field-induced filamentation in laser-beam propagation

We show that filamentation initiated by quantum fluctuations is a process that limits the intensity of a laser beam that can propagate stably through a nonlinear optical medium. We also describe the experimental signatures of this process, which allow it to be distinguished from classical processes such as filamentation induced by wave-front irregularities

Properties Of Microwave Cavities Containing Magnetic Resonant Samples

Properties of TE011 cylindrical, microwave cavities containing cylindrical samples of various radii and dielectric constants are calculated. The properties considered are the resonant frequency, quality factor (Q), relevant magnetic filling factor for spin transitions (ε), and a signal sensitivity factor (Qε) for a lossless sample. Sample sizes range from zero radius to full cavity radius with some experimental data on less than full length samples. The choice of dielectric constants ranges from one to sixteen. The data are presented in dimensionless form since they will be of use to other ESR experimentalists. It is shown that use of large samples is undesirable even if they are lossless. Furthermore, elongated cavities (D/L ratios less than one) are to be preferred over shortened cavities. © 1973 The American Institute of Physics

Using all transverse degrees of freedom in quantum communications based on a generic mode sorter

The dimension of the state space for information encoding offered by the transverse structure of light is usually limited by the finite size of apertures. The widely used orbital angular momentum (OAM) number of Laguerre-Gaussian (LG) modes in free-space communications cannot achieve the theoretical maximum transmission capacity unless the radial degree of freedom is multiplexed into the protocol. While the methodology to sort the radial quantum number has been developed, the application of radial modes in quantum communications requires an additional ability to efficiently measure the superposition of LG modes in the mutually unbiased basis. Here we develop and implement a generic mode sorter that is capable of sorting the superposition of LG modes through the use of a mode converter. As a consequence, we demonstrate an 8-dimensional quantum key distribution experiment involving all three transverse degrees of freedom: spin, azimuthal, and radial quantum numbers of photons. Our protocol presents an important step towards the goal of reaching the capacity limit of a free-space link and can be useful to other applications that involve spatial modes of photons

Nondestructive Measurement of Orbital Angular Momentum for an Electron Beam

Free electrons with a helical phase front, referred to as "twisted" electrons, possess an orbital angular momentum (OAM) and, hence, a quantized magnetic dipole moment along their propagation direction. This intrinsic magnetic moment can be used to probe material properties. Twisted electrons thus have numerous potential applications in materials science. Measuring this quantity often relies on a series of projective measurements that subsequently change the OAM carried by the electrons. In this Letter, we propose a nondestructive way of measuring an electron beam's OAM through the interaction of this associated magnetic dipole with a conductive loop. Such an interaction results in the generation of induced currents within the loop, which are found to be directly proportional to the electron's OAM value. Moreover, the electron experiences no OAM variations and only minimal energy losses upon the measurement, and, hence, the nondestructive nature of the proposed technique.Comment: 5 pages, 3 figures, and supplemental material that is comprised of text and 4 figure

Performance analysis of d-dimensional quantum cryptography under state-dependent diffraction

Standard protocols for quantum key distribution (QKD) require that the sender be able to transmit in two or more mutually unbiased bases. Here, we analyze the extent to which the performance of QKD is degraded by diffraction effects that become relevant for long propagation distances and limited sizes of apertures. In such a scenario, different states experience different amounts of diffraction, leading to state-dependent loss and phase acquisition, causing an increased error rate and security loophole at the receiver. To solve this problem, we propose a pre-compensation protocol based on pre-shaping the transverse structure of quantum states. We demonstrate, both theoretically and experimentally, that when performing QKD over a link with known, symbol-dependent loss and phase shift, the performance of QKD will be better if we intentionally increase the loss of certain symbols to make the loss and phase shift of all states same. Our results show that the pre-compensated protocol can significantly reduce the error rate induced by state-dependent diffraction and thereby improve the secure key rate of QKD systems without sacrificing the security.Comment: 10 pages, 6 figure