Scaling and complex avalanche dynamics in the Abelian sandpile model

Amir Abdolvand, Afshin Montakhab

We study the two-dimensional Abelian Sandpile Model on a square lattice of linear size L. We introduce the notion of avalanche's fine structure and compare the behavior of avalanches and waves of toppling. We show that according to the degree of complexity in the fine structure of avalanches, which is a direct consequence of the intricate superposition of the boundaries of successive waves, avalanches fall into two different categories. We propose scaling ansatz for these avalanche types and verify them numerically. We find that while the first type of avalanches (alpha) has a simple scaling behavior, the second complex type (beta) is characterized by an avalanche-size dependent scaling exponent. In particular, we define an exponent gamma to characterize the conditional probability distribution functions for these types of avalanches and show that gamma (alpha) = 0.42, while 0.7 a parts per thousand currency sign gamma (beta) a parts per thousand currency sign 1.0 depending on the avalanche size. This distinction provides a framework within which one can understand the lack of a consistent scaling behavior in this model, and directly addresses the long-standing puzzle of finite-size scaling in the Abelian sandpile model.

Noise-powered probabilistic concentration of phase information

Mario A. Usuga, Christian R. Mueller, Christoffer Wittmann, Petr Marek, Radim Filip, Christoph Marquardt, Gerd Leuchs, Ulrik L. Andersen

Phase-insensitive optical amplification of an unknown quantum state is known to be a fundamentally noisy operation that inevitably adds noise to the amplified state(1-5). However, this fundamental noise penalty in amplification can be circumvented by resorting to a probabilistic scheme as recently proposed and demonstrated in refs 6-8. These amplifiers are based on highly non-classical resources in a complex interferometer. Here we demonstrate a probabilistic quantum amplifier beating the fundamental quantum limit using a thermal-noise source and a photon-number-subtraction scheme(9). The experiment shows, surprisingly, that the addition of incoherent noise leads to a noiselessly amplified output state with a phase uncertainty below the uncertainty of the state before amplification. This amplifier might become a valuable quantum tool in future quantum metrological schemes and quantum communication protocols.

Plasmon resonances on gold nanowires directly drawn in a step-index fiber

H. K. Tyagi, H. W. Lee, P. Uebel, M. A. Schmidt, N. Joly, M. Scharrer, P. St. J. Russell

We report the successful production of high-quality gold wires, with diameters down to 260 nm, by direct fiber drawing from a gold-filled fused-silica cane. The stack-and-draw technique makes it straightforward to incorporate a conventional step-index core, adjacent to the gold wire, in the cane. In the drawn fiber, strong coupling of light from the glass core to SPP resonances on the gold wire is observed at specific well-defined wavelengths. Such embedded wires have many potential applications, for example, as nanoscale electrodes, in nonlinear optical plasmonics, and as near-field scanning optical microscope tips. (C) 2010 Optical Society of America

The Phenomenology of Ion Implantation-Induced Blistering and Thin-Layer Splitting in Compound Semiconductors

R. Singh, S. H. Christiansen, O. Moutanabbir, U. Goesele

Hydrogen and/or helium implantation-induced surface blistering and layer splitting in compound semiconductors such as InP, GaAs, GaN, AlN, and ZnO are discussed. The blistering phenomenon depends on many parameters such as the semiconductor material, ion fluence, ion energy, and implantation temperature. The optimum values of these parameters for compound semiconductors are presented. The blistering and splitting processes in silicon have been studied in detail, motivated by the fabrication of the widely used silicon-on-insulator wafers. Hence, a comparison of the blistering process in Si and compound semiconductors is also presented. This comparative study is technologically relevant since ion implantation-induced layer splitting combined with direct wafer bonding in principle allows the transfer of any type of semiconductor layer onto any foreign substrate of choice-the technique is known as the ion-cut or Smart-Cut (TM) method. For the aforementioned compound semiconductors, investigations regarding layer transfer using the ion-cut method are still in their infancy. We report feasibility studies of layer transfer by the ion-cut method for some of the most important and widely used compound semiconductors. The importance of characteristic values for successful wafer bonding such as wafer bow and surface flatness as well as roughness are discussed, and difficulties in achieving some of these values are pointed out.

EXCITON-POLARITONS IN BRAGG GRATINGS

Fabio Biancalana, Leonidas Mouchliadis, Celestino Creatore, Simon Osborne, Wolfgang Langbein

CaF2 whispering-gallery-mode-resonator stabilized-narrow-linewidth laser

B. Sprenger, H. G. L. Schwefel, Z. H. Lu, S. Svitlov, L. J. Wang

A fiber laser is stabilized by introducing a calcium fluoride (CaF2) whispering-gallery-mode resonator as a filtering element in a ring cavity. It is set up using a semiconductor optical amplifier as a gain medium. The resonator is critically coupled through prisms, and used as a filtering element to suppress the laser linewidth. A three-cornered-hat method is used and shows a stability of 10(-11) after 10 mu s. Using the self-heterodyne beat technique, the linewidth is determined to be 13 kHz. This implies an enhancement factor of 10(3) with respect to the passive cavity linewidth. (C) 2010 Optical Society of America

Bistability and stationary gap solitons in quasiperiodic photonic crystals based on Thue-Morse sequence

V. V. Grigoriev, F. Biancalana

The nonlinear properties of quasiperiodic photonic crystals based on the Thue-Morse sequence are investigated. The intrinsic asymmetry of these one-dimensional structures for odd generation numbers results in bistability thresholds which are sensitive to propagation direction. Along with resonances of perfect transmission, this feature allows to obtain strongly nonreciprocal propagation and to create an all-optical diode. The efficiency of two schemes is compared: passive and active when an additional short pump signal is applied to the system. The existence of stationary gap solitons in quasiperiodic photonic crystals is shown numerically, and their difference from the Bragg case is emphasized. (C) 2010 Elsevier B.V. All rights reserved.

Optimized generation of heralded Fock states using parametric down-conversion

Agata M. Branczyk, T. C. Ralph, Wolfram Helwig, Christine Silberhorn

The generation of heralded pure Fock states via spontaneous parametric down-conversion (PDC) relies on perfect photon-number correlations in the output modes. Correlations in any other degree of freedom, however, degrade the purity of the heralded state. In this paper, we investigate spectral entanglement between the two output modes of a periodically poled waveguide. With the intent of generating heralded one-and two-photon Fock states, we expand the output state of the PDC to second order in photon number. We explore the effects of spectral filtering and inefficient detection, of the heralding mode, on the count rate, g((2)), and purity of the heralded state, as well as the fidelity between the resulting state and an ideal Fock state. We find that filtering can decrease spectral correlations, however, at the expense of the count rate and increased photon-number mixedness in the heralded output state. As a physical example, we model a type II PP-KTP waveguide pumped by lasers at wavelengths of 400 nm, 788 nm and 1.93 mu m. The latter two allow the fulfillment of extended phase-matching conditions in an attempt to eliminate spectral correlations in the PDC output state without the use of filtering; however, we find that, even in these cases, some filtering is needed to achieve states of very high purity.

A bridge between the single-photon and squeezed-vacuum states

Nitin Jain, S. R. Huisman, Erwan Bimbard, A. I. Lvovsky

The two modes of the Einstein-Podolsky-Rosen quadrature entangled state generated by parametric down-conversion interfere on a beam splitter of variable splitting ratio. Detection of a photon in one of the beam splitter output channels heralds preparation of a signal state in the other, which is characterized using homodyne tomography. By controlling the beam splitting ratio, the signal state can be chosen anywhere between the single-photon and squeezed state. (C) 2010 Optical Society of America

A note on quantum error correction with continuous variables

Peter van Loock

We demonstrate that continuous-variable quantum error correction based on Gaussian ancilla states and Gaussian operations (for encoding, syndrome extraction, and recovery) can be very useful to suppress the effect of non-Gaussian error channels. For a certain class of stochastic error models, reminiscent of those typically considered in the qubit case, quantum error correction codes designed for single-channel errors may enhance the transfer fidelities even when errors occur in every channel employed for transmitting the encoded state. In fact, in this case, the error-correcting capability of the continuous-variable scheme turns out to be higher than that of its discrete-variable analogues.