Robustness of Majorana Fermion induced Fractional Josephson Effect

It is shown in previous works that the coupling between two Majorana end states in superconducting quantum wires leads to fractional Josephson effect. However, in realistic experimental conditions, multiple bands of the wires are occupied and the Majorana end states are accompanied by other fermionic end states. This raises the question concerning the robustness of fractional Josephson effect in these situations. In this work, we show that the absence of the avoided energy crossing which gives rise to the fractional Josephson effect is robust, even when the Majorana fermions are coupled with arbitrary strengths to other fermions. Moreover, we calculate the temperature dependence of the fractional Josephson current and show that it is suppressed by thermal excitations to the other fermion bound states.Comment: 4+ pages, 3 figure

Coherent control of spin squeezing

We report an interaction that controls spin squeezing in a collection of spin 1/2 particles. We describe how spin squeezing can be generated and maintained in time. Our scheme can be applied to control the spin squeezing in a Bose condensate with two internal spin states.Comment: 3 pages, 2 figure

Topological Excitations in Spinor Bose-Einstein Condensates

We investigate the properties of skyrmion in the ferromagnetic state of spin-1 Bose-Einstein condensates by means of the mean-field theory and show that the size of skyrmion is fixed to the order of the healing length. It is shown that the interaction between two skyrmions with oppositely rotating spin textures is attractive when their separation is large, following a unique power-law behavior with a power of -7/2.Comment: 4 pages, 5 figure

Shot Noise in Anyonic Mach-Zehnder Interferometer

We show how shot noise in an electronic Mach-Zehnder interferometer in the fractional quantum Hall regime probes the charge and statistics of quantum Hall quasiparticles. The dependence of the noise on the magnetic flux through the interferometer allows for a simple way to distinguish Abelian from non-Abelian quasiparticle statistics. In the Abelian case, the Fano factor (in units of the electron charge) is always lower than unity. In the non-Abelian case, the maximal Fano factor as a function of the magnetic flux exceeds one.Comment: references adde

Quantum Dot in 2D Topological Insulator: The Two-channel Kondo Fixed Point

In this work, a quantum dot couples to two helical edge states of a 2D topological insulator through weak tunnelings is studied. We show that if the electron interactions on the edge states are repulsive, with Luttinger liquid parameter $K < 1$, the system flows to a stable two-channel fixed point at low temperatures. This is in contrast to the case of a quantum dot couples to two Luttinger liquid leads. In the latter case, a strong electron-electron repulsion is needed, with $K<1/2$, to reach the two-channel fixed point. This two-channel fixed point is described by a boundary Sine-Gordon Hamiltonian with a $K$ dependent boundary term. The impurity entropy at zero temperature is shown to be $\ln\sqrt{2K}$. The impurity specific heat is $C \propto T^{\frac{2}{K}-2}$ when $2/3 < K < 1$, and $C \propto T$ when $K<2/3$. We also show that the linear conductance across the two helical edges has non-trivial temperature dependence as a result of the renormalization group flow.Comment: 4+\epsilon page

Zero-bias peaks in spin-orbit coupled superconducting wires with and without Majorana end-states

One of the simplest proposed experimental probes of a Majorana bound-state is a quantized (2e^2/h) value of zero-bias tunneling conductance. When temperature is somewhat larger than the intrinsic width of the Majorana peak, conductance is no longer quantized, but a zero-bias peak can remain. Such a non-quantized zero-bias peak has been recently reported for semiconducting nanowires with proximity induced superconductivity. In this paper we analyze the relation of the zero-bias peak to the presence of Majorana end-states, by simulating the tunneling conductance for multi-band wires with realistic amounts of disorder. We show that this system generically exhibits a (non-quantized) zero-bias peak even when the wire is topologically trivial and does not possess Majorana end-states. We make comparisons to recent experiments, and discuss the necessary requirements for confirming the existence of a Majorana state.Comment: 5 pages, 4 Figure

On The Complexity and Completeness of Static Constraints for Breaking Row and Column Symmetry

We consider a common type of symmetry where we have a matrix of decision variables with interchangeable rows and columns. A simple and efficient method to deal with such row and column symmetry is to post symmetry breaking constraints like DOUBLELEX and SNAKELEX. We provide a number of positive and negative results on posting such symmetry breaking constraints. On the positive side, we prove that we can compute in polynomial time a unique representative of an equivalence class in a matrix model with row and column symmetry if the number of rows (or of columns) is bounded and in a number of other special cases. On the negative side, we show that whilst DOUBLELEX and SNAKELEX are often effective in practice, they can leave a large number of symmetric solutions in the worst case. In addition, we prove that propagating DOUBLELEX completely is NP-hard. Finally we consider how to break row, column and value symmetry, correcting a result in the literature about the safeness of combining different symmetry breaking constraints. We end with the first experimental study on how much symmetry is left by DOUBLELEX and SNAKELEX on some benchmark problems.Comment: To appear in the Proceedings of the 16th International Conference on Principles and Practice of Constraint Programming (CP 2010

Rational engineering of nanoporous anodic alumina optical bandpass filters

First published online 07 Jul 2016Herein, we present a rationally designed advanced nanofabrication approach aiming at producing a new type of optical bandpass filters based on nanoporous anodic alumina photonic crystals. The photonic stop band of nanoporous anodic alumina (NAA) is engineered in depth by means of a pseudo-stepwise pulse anodisation (PSPA) approach consisting of pseudo-stepwise asymmetric current density pulses. This nanofabrication method makes it possible to tune the transmission bands of NAA at specific wavelengths and bandwidths, which can be broadly modified across the UV-visible-NIR spectrum through the anodisation period (i.e. time between consecutive pulses). First, we establish the effect of the anodisation period as a means of tuning the position and width of the transmission bands of NAA across the UV-visible-NIR spectrum. To this end, a set of nanoporous anodic alumina bandpass filters (NAA-BPFs) are produced with different anodisation periods, ranging from 500 to 1200 s, and their optical properties (i.e. characteristic transmission bands and interferometric colours) are systematically assessed. Then, we demonstrate that the rational combination of stacked NAA-BPFs consisting of layers of NAA produced with different PSPA periods can be readily used to create a set of unique and highly selective optical bandpass filters with characteristic transmission bands, the position, width and number of which can be precisely engineered by this rational anodisation approach. Finally, as a proof-of-concept, we demonstrate that the superposition of stacked NAA-BPFs produced with slight modifications of the anodisation period enables the fabrication of NAA-BPFs with unprecedented broad transmission bands across the UV-visible-NIR spectrum. The results obtained from our study constitute the first comprehensive rationale towards advanced NAA-BPFs with fully controllable photonic properties. These photonic crystal structures could become a promising alternative to traditional optical bandpass filters based on glass and plastic.Abel Santos, Taj Pereira, Cheryl Suwen Law and Dusan Losi