Quantum simulation of topological Majorana bound states and their universal quantum operations using charge-qubit arrays

Majorana bound states have been a focus of condensed matter research for their potential applications in topological quantum computation. Here we utilize two charge-qubit arrays to explicitly simulate a DIII class one-dimensional superconductor model where Majorana end states can appear. Combined with one braiding operation, universal single-qubit operations on a Majorana-based qubit can be implemented by a controllable inductive coupling between two charge qubits at the ends of the arrays. We further show that in a similar way, a controlled-NOT gate for two topological qubits can be simulated in four charge-qubit arrays. Although the current scheme may not truly realize topological quantum operations, we elaborate that the operations in charge-qubit arrays are indeed robust against certain local perturbations.Comment: 5 pages, 3 figure

Correlation evolution and monogamy of two geometric quantum discords in multipartite systems

We explore two different geometric quantum discords defined respectively via the trace norm (GQD-1) and Hilbert-Schmidt norm (GQD-2) in multipartite systems. A rigorous hierarchy relation is revealed for the two GQDs in a class of symmetric two-qubit $X$-shape states. For multiqubit pure states, it is found that both GQDs are related to the entanglement concurrence, with the hierarchy relation being saturated. Furthermore, we look into a four-partite dynamical system consisting of two cavities interacting with independent reservoirs. It is found that the GQD-2 can exhibit various sudden change behaviours, while the GQD-1 only evolves asymptotically, with the two GQDs exhibiting different monogamous properties.Comment: 5 pages, 3 figure

Modeling Light-Extraction Characteristics of Packaged Light-Emitting Diodes

We employ a Monte Carlo ray-tracing technique to model light-extraction characteristics of light-emitting diodes. By relaxing restrictive assumptions on photon traversal history, our method improves upon available analytical models for estimating light-extraction efficiencies from bare LED chips, and enhances modeling capabilities by realistically treating the various processes which photons can encounter in a packaged LED. Our method is not only capable of calculating extraction efficiencies, but can also provide extensive statistical information on photon extraction processes, and predict LED spatial emission characteristics

Interface roughness effects on transport in tunnel structures

Direct simulations of interface roughness effects on transport properties of tunnel structures are performed using the planar supercell stack method. The method allows for the inclusion of realistic three-dimensional rough interfacial geometries in transport calculations. For double barrier resonant tunneling structures, we used our method to analyze the effect of roughness at each of the four interfaces, and to test for sensitivity of transport properties to island size and height. Our simulations yields the following conclusions: (1) We find that scattering of off-resonance states into on-resonance states provides the dominant contribution to interface roughness assisted tunneling. Analyses of scattering strength sensitivity to interface layer configurations reveals preferential scattering into Delta k parallel to approximate to 2 pi/lambda states, where lambda is the island size. (2) We find that roughness at interfaces adjacent to the quantum well can cause lateral localization of wave functions, which increases with island size and depth. Lateral localization can result in the broadening and shifting of transmission resonances, and the introduction of preferential transmission paths. In structures with wide and tall islands, it is possible to find localization over "islands" as well as localization over "oceans." (3) The leading rough interface is the strongest off-resonance scatterer, while rough interfaces adjacent to quantum well are the strongest on-resonance scatterers. The trailing interface is the weakest scatterer

Spin-charge separation: From one hole to finite doping

In the presence of nonlocal phase shift effects, a quasiparticle can remain topologically stable even in a spin-charge separation state due to the confinement effect introduced by the phase shifts at finite doping. True deconfinement only happens in the zero-doping limit where a bare hole can lose its integrity and decay into holon and spinon elementary excitations. The Fermi surface structure is completely different in these two cases, from a large band-structure-like one to four Fermi points in one-hole case, and we argue that the so-called underdoped regime actually corresponds to a situation in between.Comment: 4 pages, 2 figures, presented in M2S-HTSC-VI conference (2000

Description of bulk inversion asymmetry in the effective-bond-orbital model

We have extended the effective-bond-orbital model (EBOM) method [Y. C. Chang, Phys. Rev. B 37, 8215 (1988)] to include the effects of the bulk inversion asymmetry (BIA) present in zinc blendes. This is accomplished without adding to the number of basis states or extending the range of interaction. We have also investigated a variant form of the EBOM proposed in the original formulation that offers improved zone-center behavior, but may also generate spurious solutions in heterostructure calculations due to poor description of bulk zone-boundary band structure. We offer suggestions for avoiding this problem so that this variant form of EBOM may be used safely. In general, we find that the addition of BIA effects in EBOM results in improved descriptions of zone-center band structure, but also in a loss of accuracy far from the Brillouin-zone center. We illustrate the use of the BIA extension with band-structure calculations for bulk GaSb. We show that the spin splitting predicted by the extended EBOM method for an AlSb/GaSb superlattice is in good agreement with k·p calculations that include BIA effects

Numerical spurious solutions in the effective mass approximation

We have characterized a class of spurious solutions that appears when using the finite difference method to solve the effective mass approximation equations. We find that the behavior of these solutions as predicted by our model shows excellent agreement with numerical results. Using this interpretation we find a set of analytical expressions for conditions that the Luttinger parameters must satisfy to avoid spurious solutions. Finally, we use these conditions to check commonly used sets of parameters for their potential for generating this class of spurious solutions

The Finite Basis Problem for Kiselman Monoids

In an earlier paper, the second-named author has described the identities holding in the so-called Catalan monoids. Here we extend this description to a certain family of Hecke--Kiselman monoids including the Kiselman monoids $\mathcal{K}_n$. As a consequence, we conclude that the identities of $\mathcal{K}_n$ are nonfinitely based for every $n\ge 4$ and exhibit a finite identity basis for the identities of each of the monoids $\mathcal{K}_2$ and $\mathcal{K}_3$. In the third version a question left open in the initial submission has beed answered.Comment: 16 pages, 1 table, 1 figur