Time fractional Schrodinger equation

The Schrodinger equation is considered with the first order time derivative changed to a Caputo fractional derivative, the time fractional Schrodinger equation. The resulting Hamiltonian is found to be non-Hermitian and non-local in time. The resulting wave functions are thus not invariant under time reversal. The time fractional Schrodinger equation is solved for a free particle and for a potential well. Probability and the resulting energy levels are found to increase over time to a limiting value depending on the order of the time derivative. New identities for the Mittag-Leffler function are also found and presented in an appendix.Comment: 23 page

Radiation effects in silicon solar cells Quarterly report

Effect of lithium on production and annealing of damage in silico

Radiation effects in silicon solar cells Quarterly progress report, 1 Jul. - 30 Sep. 1970

Defects responsible for degradation in output of silicon solar cells irradiated by space radiatio

Trapping of Rydberg Atoms in Tight Magnetic Microtraps

We explore the possibility to trap Rydberg atoms in tightly confining magnetic microtraps. The trapping frequencies for Rydberg atoms are expected to be influenced strongly by magnetic field gradients. We show that there are regimes where Rydberg atoms can be trapped. Moreover, we show that so-called magic trapping conditions can be found for certain states of rubidium, where both Rydberg atoms and ground state atoms have the same trapping frequencies. Magic trapping is highly beneficial for implementing quantum gate operations that require long operation times

Single-shot readout of electron spin states in a quantum dot using spin-dependent tunnel rates

We present a method for reading out the spin state of electrons in a quantum dot that is robust against charge noise and can be used even when the electron temperature exceeds the energy splitting between the states. The spin states are first correlated to different charge states using a spin dependence of the tunnel rates. A subsequent fast measurement of the charge on the dot then reveals the original spin state. We experimentally demonstrate the method by performing read-out of the two-electron spin states, achieving a single-shot visibility of more than 80%. We find very long triplet-to-singlet relaxation times (up to several milliseconds), with a strong dependence on in-plane magnetic field.Comment: 4 pages, 4 figure

Towards the topological quantization of classical mechanics

We consider the method of topological quantization for conservative systems with a finite number of degrees of freedom. Maupertuis' formalism for classical mechanics provides an appropriate scenario which permit us to adapt the method of topological quantization, originally formulated for gravitational field configurations. We show that any conservative system in classical mechanics can be associated with a principal fiber bundle. As an application of topological quantization we derive expressions for the topological spectra of some simple mechanical systems and show that they reproduce the discrete behavior of the corresponding canonical spectra

Fractional Hamilton formalism within Caputo's derivative

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained. Using an example, it is shown that the canonical fractional Hamiltonian and the fractional Euler-Lagrange formulations lead to the same set of equations.Comment: 8 page

Effects of Natural Scene Inversion on Visual-evoked Brain Potentials and Pupillary Responses: A Matter of Effortful Processing of Unfamiliar Configurations

The inversion of a picture of a face hampers the accuracy and speed at which observers can perceptually process it. Event-related potentials and pupillary responses, successfully used as biomarkers of face inversion in the past, suggest that the perception of visual features, that are organized in an unfamiliar manner, recruits demanding additional processes. However, it remains unclear whether such inversion effects generalize beyond face stimuli and whether indeed more mental effort is needed to process inverted images. Here we aimed to study the effects of natural scene inversion on visual evoked potentials and pupil dilations. We simultaneously measured responses of 47 human participants to presentations of images showing upright or inverted natural scenes. For inverted scenes, we observed relatively stronger occipito-temporo-parietal N1 peak amplitudes and larger pupil dilations (on top of an initial orienting response) than for upright scenes. This study revealed neural and physiological markers of natural scene inversion that are in line with inversion effects of other stimulus types and demonstrates the robustness and generalizability of the phenomenon that unfamiliar configurations of visual content require increased processing effort

Magnetic-film atom chip with 10 μ\mum period lattices of microtraps for quantum information science with Rydberg atoms

We describe the fabrication and construction of a setup for creating lattices of magnetic microtraps for ultracold atoms on an atom chip. The lattice is defined by lithographic patterning of a permanent magnetic film. Patterned magnetic-film atom chips enable a large variety of trapping geometries over a wide range of length scales. We demonstrate an atom chip with a lattice constant of 10 $\mu$m, suitable for experiments in quantum information science employing the interaction between atoms in highly-excited Rydberg energy levels. The active trapping region contains lattice regions with square and hexagonal symmetry, with the two regions joined at an interface. A structure of macroscopic wires, cut out of a silver foil, was mounted under the atom chip in order to load ultracold $^{87}$Rb atoms into the microtraps. We demonstrate loading of atoms into the square and hexagonal lattice sections simultaneously and show resolved imaging of individual lattice sites. Magnetic-film lattices on atom chips provide a versatile platform for experiments with ultracold atoms, in particular for quantum information science and quantum simulation.Comment: 7 pages, 7 figure