Controlling Photons in a Box and Exploring the Quantum to Classical Boundary (Nobel Lecture)

Microwave photons trapped in a superconducting cavity constitute an ideal system to realize some of the thought experiments imagined by the founding fathers of quantum physics. The interaction of these trapped photons with Rydberg atoms crossing the cavity illustrates fundamental aspects of measurement theory. The experiments performed with this “photon box” at Ecole Normale Supérieure (ENS) belong to the domain of quantum optics called “Cavity Quantum Electrodynamics”. We have realized the non‐destructive counting of photons, the recording of field quantum jumps, the preparation and reconstruction of “Schrödinger cat” states of radiation and the study of their decoherence, which provides a striking illustration of the transition from the quantum to the classical world. These experiments have also led to the demonstration of basic steps in quantum information processing, including the deterministic entanglement of atoms and the realization of quantum gates using atoms and photons as quantum bits. This lecture starts by an introduction stressing the connection between the ENS photon box and the ion trap experiments of David Wineland, whose accompanying lecture recalls his own contribution to the field of single particle control. I give then a personal account of the early days of Cavity Quantum Electrodynamics before describing the main experiments performed at ENS during the last twenty years and concluding by a discussion comparing our work to other researches dealing with the control of single quantum particles.     

Challenges in the Highly Selective [3 + 1]-Cycloaddition of an Enoldiazoacetamide to Form a Donor–Acceptor Cis-Cyclobutenecarboxamide

A substituted donor–acceptor cyclobutenecarboxamide is synthesized with modest enantiocontrol through a chiral copper(I) complex catalyzed [3 + 1]-cycloaddition reaction of α-acyl diphenylsulfur ylides with 3-siloxy-2-diazo-3-butenamides. With a methyl substituent on the 4-position of the 3-butenamide, the cis-vicinal-3,4-disubstituted cyclobutenecarboxamide is formed with >20:1 diastereocontrol. Donor-acceptor 3-methyl-2-siloxycyclopropenecarboxamide is rapidly formed from the reactant enoldiazoamide and undergoes catalytic ring opening to give only the Z-γ-substituted metallo-enolcarbene. Elimination from 3-siloxy-2-diazo-3-pentenamide to form the conjugated 3-siloxy-2,4-pentadienamide is competitive but minimized at low temperature.     

CBS还原合成手性1-苯乙醇实验设计*

将学科热点之一催化不对称合成策略引入实验教学中,通过CBS还原制备手性醇。实验以苯乙酮为原料,还原得到粗产物手性1-苯乙醇,经制备色谱仪分离提纯,气相色谱和自动旋光仪表征产物的光学性质。实验为综合型有机化学实验,通过此实验,学生在掌握手性醇合成原理与方法的同时,进一步学习手套箱、气相色谱、制备色谱仪、自动旋光仪等新技术,以提升学生综合科研素质。     

基于kinect和unity的虚拟手抓取碰撞检测算法

针对目前碰撞检测算法效率低精度差的问题,提出了一种改进的层次方向包围盒（OBB）算法。首先通过位置关系判断虚拟手是否在物体包围球的邻近区域,然后用OBB和八叉树算法进行详细的碰撞检测,最后利用离散点到虚拟手简化面的矢量计算法实现精确的碰撞检测。实验结果表明,随着三维物体基元数目的增多,这种由粗略到精确递进的检测方式极大的提高了碰撞检测的效率和精度,具有可行性。该算法适用于任何复杂场景中刚体结构模型的碰撞检测,在运行时候不存在滞后情况,显示流畅,而且碰撞检测精度高,完全能够满足虚拟环境实时性和精确性的要求。     

Multi-Fractal Formalism for Quasi-Self-Similar Functions

The study of multi-fractal functions has proved important in several domains of physics. Some physical phenomena such as fully developed turbulence or diffusion limited aggregates seem to exhibit some sort of self-similarity. The validity of the multi-fractal formalism has been proved to be valid for self-similar functions. But, multi-fractals encountered in physics or image processing are not exactly self-similar. For this reason, we extend the validity of the multi-fractal formalism for a class of some non-self-similar functions. Our functions are written as the superposition of similar structures at different scales, reminiscent of some possible modelization of turbulence or cascade models. Their expressions look also like wavelet decompositions. For the computation of their spectrum of singularities, it is unknown how to construct Gibbs measures. However, it suffices to use measures constructed according the Frostman's method. Besides, we compute the box dimension of the graphs.     

Helly-type theorems for hollow axis-aligned boxes

A hollow axis-aligned box is the boundary of the cartesian product of compact intervals in . We show that for , if any of a collection of hollow axis-aligned boxes have non-empty intersection, then the whole collection has non-empty intersection; and if any of a collection of hollow axis-aligned rectangles in have non-empty intersection, then the whole collection has non-empty intersection. The values for and for are the best possible in general. We also characterize the collections of hollow boxes which would be counterexamples if were lowered to , and to , respectively.

     

Existence and Limiting Behavior of Trajectories Associated with P0-equations

Given a continuous P₀-function F : Rⁿ Rⁿ, we describe a method of constructing trajectories associated with the P₀-equation F(x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P₀-function lead to P₀-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P₀-equations when the underlying function is P₀. To generate the trajectories, we perturb the given P₀-function F to a P-function F(x, ); unique solutions of F(x, ) = 0 as varies over an interval in (0, ) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem.     

Finite-element modelling of soil-geogrid interaction dealing with the pullout behaviour of geogrids

A two dimensional plane-stress finite-element type of analysis is presented to predict the behaviour of geogrids embedded in sand under pullout loading conditions. In the analysis the interactions between soil and geogrid are simulated by non-linear springs. The stiffnesses of the springs can be determined from simple tests in a specially designed pullout box. The proposed finite element (FE) analysis is applied to interpret test results from a large scale pullout test rig. The predicted behaviour of the geogrid under pullout load agrees well with the observed data including the load-displacement properties, the displacement distribution along the longitudinal direction and the mobilisation of the frictional and bearing resistance.     

Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems

We construct and analyze a mixed finite volume method on quadrilateral grids for elliptic problems written as a system of two first order PDEs in the state variable (e.g., pressure) and its flux (e.g., Darcy velocity). An important point is that no staggered grids or covolumes are used to stabilize the system. Only a single primary grid system is adopted, and the degrees of freedom are imposed on the interfaces. The approximate flux is sought in the lowest-order Raviart-Thomas space and the pressure field in the rotated- nonconforming space. Furthermore, we demonstrate that the present finite volume method can be interpreted as a rotated- nonconforming finite element method for the pressure with a simple local recovery of flux. Numerical results are presented for a variety of problems which confirm the usefulness and effectiveness of the method.

     

利用TEM对Si基片与MgO基片上生长的薄膜特性的研究

对生长在Si和MgO单晶基片上的不同厚度的单层NbN薄膜、双层薄膜AlN/NbN以及三层薄膜NbN/AlN/NbN应用透射电子显微镜(Transmission Electron Microscope,TEM)技术进行了分析研究,对这几种薄膜样品的微观结构、薄膜厚度以及各个边界的一些直观细节给出了较为清晰的图像。由透射电子显微镜的电子衍射图案计算了薄膜和单晶衬底的晶格常数,并与我们以前采用X射线衍射技术分析的结果进行了比较,结果有很好的吻合。