Electron interferometry in quantum Hall regime: Aharonov-Bohm effect of interacting electrons

An apparent h/fe Aharonov-Bohm flux period, where f is an integer, has been reported in coherent quantum Hall devices. Such sub-period is not expected for non-interacting electrons and thus is thought to result from interelectron Coulomb interaction. Here we report experiments in a Fabry-Perot interferometer comprised of two wide constrictions enclosing an electron island. By carefully tuning the constriction front gates, we find a regime where interference oscillations with period h/2e persist throughout the transition between the integer quantum Hall plateaus 2 and 3, including half-filling. In a large quantum Hall sample, a transition between integer plateaus occurs near half-filling, where the bulk of the sample becomes delocalized and thus dissipative bulk current flows between the counterpropagating edges ("backscattering"). In a quantum Hall constriction, where conductance is due to electron tunneling, a transition between forward- and back-scattering is expected near the half-filling. In our experiment, neither period nor amplitude of the oscillations show a discontinuity at half-filling, indicating that only one interference path exists throughout the transition. We also present experiments and an analysis of the front-gate dependence of the phase of the oscillations. The results point to a single physical mechanism of the observed conductance oscillations: Aharonov-Bohm interference of interacting electrons in quantum Hall regime.Comment: 10 pages, 4 Fig

Phase-driven interaction of widely separated nonlinear Schr\"odinger solitons

We show that, for the 1d cubic NLS equation, widely separated equal amplitude in-phase solitons attract and opposite-phase solitons repel. Our result gives an exact description of the evolution of the two solitons valid until the solitons have moved a distance comparable to the logarithm of the initial separation. Our method does not use the inverse scattering theory and should be applicable to nonintegrable equations with local nonlinearities that support solitons with exponentially decaying tails. The result is presented as a special case of a general framework which also addresses, for example, the dynamics of single solitons subject to external forces

DeepKSPD: Learning Kernel-matrix-based SPD Representation for Fine-grained Image Recognition

Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by modelling the nonlinearity in the local descriptor set. Nevertheless, neither the descriptors nor the kernel matrix is deeply learned. Worse, they are considered separately, hindering the pursuit of an optimal SPD representation. This work proposes a deep network that jointly learns local descriptors, kernel-matrix-based SPD representation, and the classifier via an end-to-end training process. We derive the derivatives for the mapping from a local descriptor set to the SPD representation to carry out backpropagation. Also, we exploit the Daleckii-Krein formula in operator theory to give a concise and unified result on differentiating SPD matrix functions, including the matrix logarithm to handle the Riemannian geometry of kernel matrix. Experiments not only show the superiority of kernel-matrix-based SPD representation with deep local descriptors, but also verify the advantage of the proposed deep network in pursuing better SPD representations for fine-grained image recognition tasks

Configuration-Space Location of the Entanglement between Two Subsystems

In this paper we address the question: where in configuration space is the entanglement between two particles located? We present a thought-experiment, equally applicable to discrete or continuous-variable systems, in which one or both parties makes a preliminary measurement of the state with only enough resolution to determine whether or not the particle resides in a chosen region, before attempting to make use of the entanglement. We argue that this provides an operational answer to the question of how much entanglement was originally located within the chosen region. We illustrate the approach in a spin system, and also in a pair of coupled harmonic oscillators. Our approach is particularly simple to implement for pure states, since in this case the sub-ensemble in which the system is definitely located in the restricted region after the measurement is also pure, and hence its entanglement can be simply characterised by the entropy of the reduced density operators. For our spin example we present results showing how the entanglement varies as a function of the parameters of the initial state; for the continuous case, we find also how it depends on the location and size of the chosen regions. Hence we show that the distribution of entanglement is very different from the distribution of the classical correlations.Comment: RevTex, 12 pages, 9 figures (28 files). Modifications in response to journal referee

Sliding of Electron Crystal of Finite Size on the Surface of Superfluid He-4 Confined in a Microchannel

We present a new study of the nonlinear transport of a two-dimensional electron crystal on the surface of liquid helium confined in a 10 micrometer-wide channel in which the effective length of the crystal can be varied from 10 to 215 micrometers. At low driving voltages, the moving electron crystal is strongly coupled to deformation of the liquid surface arising from resonant excitation of surface capillary waves, ripplons, while at higher driving voltages the crystal decouples from the deformation. We find strong dependence of the decoupling threshold of the driving electric field acting on the electrons, on the size of the crystal. In particular, the threshold electric field significantly decreases when the length of the crystal becomes shorter than 25 micrometers. We explain this effect as arising from weakening of surface deformations due to radiative loss of resonantly-excited ripplons from an electron crystal of finite size, and we account for the observed effect using an instructive analytical model.Comment: 5 figure

Entanglement and quantum phase transition in the extended Hubbard model

We study quantum entanglement in one-dimensional correlated fermionic system. Our results show, for the first time, that entanglement can be used to identify quantum phase transitions in fermionic systems.Comment: 5 pages, 4 figure