Identifying the orbital angular momentum of light based on atomic ensembles

We propose a scheme to distinguish the orbital angular momentum state of the Laguerre-Gaussian (LG) beam based on the electromagnetically induced transparency modulated by a microwave field in atomic ensembles. We show that the transverse phase variation of a probe beam with the LG mode can be mapped into the spatial intensity distribution due to the change of atomic coherence caused by the microwave. The proposal may provide a useful tool for studying higher-dimensional quantum information based on atomic ensembles.Comment: 4 pages, 4 figure

Valence band offset of InN/BaTiO3 heterojunction measured by X-ray photoelectron spectroscopy

X-ray photoelectron spectroscopy has been used to measure the valence band offset of the InN/BaTiO(3 )heterojunction. It is found that a type-I band alignment forms at the interface. The valence band offset (VBO) and conduction band offset (CBO) are determined to be 2.25 ± 0.09 and 0.15 ± 0.09 eV, respectively. The experimental VBO data is well consistent with the value that comes from transitivity rule. The accurate determination of VBO and CBO is important for use of semiconductor/ferrroelectric heterojunction multifunctional devices

Investigation of cracks in GaN films grown by combined hydride and metal organic vapor-phase epitaxial method

Cracks appeared in GaN epitaxial layers which were grown by a novel method combining metal organic vapor-phase epitaxy (MOCVD) and hydride vapor-phase epitaxy (HVPE) in one chamber. The origin of cracks in a 22-μm thick GaN film was fully investigated by high-resolution X-ray diffraction (XRD), micro-Raman spectra, and scanning electron microscopy (SEM). Many cracks under the surface were first observed by SEM after etching for 10 min. By investigating the cross section of the sample with high-resolution micro-Raman spectra, the distribution of the stress along the depth was determined. From the interface of the film/substrate to the top surface of the film, several turnings were found. A large compressive stress existed at the interface. The stress went down as the detecting area was moved up from the interface to the overlayer, and it was maintained at a large value for a long depth area. Then it went down again, and it finally increased near the top surface. The cross-section of the film was observed after cleaving and etching for 2 min. It was found that the crystal quality of the healed part was nearly the same as the uncracked region. This indicated that cracking occurred in the growth, when the tensile stress accumulated and reached the critical value. Moreover, the cracks would heal because of high lateral growth rate

Distributionally robust shortfall risk optimization model and its approximation

Utility-based shortfall risk measures (SR)have received increasing attention over the past few years for their potential to quantify the risk of large tail losses more effectively than conditional value at risk.In this paper, we consider a distributionally robust version of the shortfall risk measure (DRSR) where the true probability distribution is unknown and the worst distribution from an ambiguity set of distributions} is used to calculate the SR. We start by showing that the DRSR is a convex risk measure and under some special circumstance a coherent risk measure.We then move on to study an optimization problem with the objective of minimizing the DRSR of a random function and investigate numerical tractability of the optimization problem with the ambiguity set being constructed through $\phi$-divergence ball and Kantorovich ball. In the case when the nominal distribution in the balls is an empirical distribution constructed through iid samples,we quantify convergence of the ambiguity sets to the true probability distribution as the sample size increases under the Kantorovich metric and consequently the optimal values of the corresponding DRSR problems. Specifically, we show that the error of the optimal value is linearly bounded by the error of each of the approximate ambiguity sets and subsequently derive a confidence interval of the optimal value under each of the approximation schemes. Some preliminary numerical test results are reported for the proposed modeling and computational schemes

Convergence analysis for mathematical programs with distributionally robust chance constraint

Convergence analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and the optimal solutions and research on this topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance constraints where the true probability distribution is unknown, but it is possible to construct an ambiguity set of probability distributions and the chance constraint is based on the most conservative selection of probability distribution from the ambiguity set. The convergence analysis focuses on impact of the variation of the ambiguity set on the optimal value and the optimal solutions. We start by deriving general convergence results under abstract conditions such as continuity of the robust probability function and uniform convergence of the robust probability functions and followed with detailed analysis of these conditions. Two sufficient conditions have been derived with one applicable to both continuous and discrete probability distribution and the other to continuous distribution. Case studies are carried out for ambiguity sets being constructed through moments and samples.Read More: https://epubs.siam.org/doi/10.1137/15M1036592<br/

Probability approximation schemes for stochastic programs with distributionally robust second order dominance constraints

Since the pioneering work by Dentcheva and Ruszczy?ski [Optimization with stochastic dominance constraints, SIAM J. Optim. 14 (2003), pp. 548–566], stochastic programs with second-order dominance constraints (SPSODC) have received extensive discussions over the past decade from theory of optimality to numerical schemes and practical applications. In this paper, we investigate discrete approximation of SPSODC when (a) the true probability is known but continuously distributed and (b) the true probability distribution is unknown but it lies within an ambiguity set of distributions. Differing from the well-known Monte Carlo discretization method, we propose a deterministic discrete approximation scheme due to Pflug and Pichler [Approximations for Probability Distributions and Stochastic Optimization Problems, International Series in Operations Research &amp; Management Science, Vol. 163, Springer, New York, 2011, pp. 343–387] and demonstrate that the discrete probability measure and the ambiguity set of discrete probability measures approximate their continuous counterparts under the Kantorovich metric. Stability analysis of the optimal value and optimal solutions of the resulting discrete optimization problems is presented and some comparative numerical test results are reported