Mesoscopic Superposition of States with Sub-Planck Structures in Phase Space

We propose a method using the dispersive interaction between atoms and a high quality cavity to realize the mesoscopic superposition of coherent states which would exhibit sub-Planck structures in phase space. In particular we focus on a superposition involving four coherent states. We show interesting interferences in the conditional measurements involving two atoms.Comment: 4-page 3-figur

Thermo-Chemical Surface Hardening Treatment of Steels

Case Carburising is a process in which austenised ferrous metal is brought into contact with an environment of sufficient carbon potential to cause absorption of carbon at the surface, and by diffusion, to create a carbon concentration gradient between the surface and interior of the metal. The addition of carbon referen-tially to the surface layers of the steels followed by proper heat treatment develops the hard abrasive, wear resistant surface and as the core remains comparatively soft and tough the component as a whole shows high impact strength. Due to the residual stress pattern developed during the process the fatigue strength also improves

Quantum random walk of two photons in separable and entangled state

We discuss quantum random walk of two photons using linear optical elements. We analyze the quantum random walk using photons in a variety of quantum states including entangled states. We find that for photons initially in separable Fock states, the final state is entangled. For polarization entangled photons produced by type II downconverter, we calculate the joint probability of detecting two photons at a given site. We show the remarkable dependence of the two photon detection probability on the quantum nature of the state. In order to understand the quantum random walk, we present exact analytical results for small number of steps like five. We present in details numerical results for a number of cases and supplement the numerical results with asymptotic analytical results

Computing Similarity between a Pair of Trajectories

With recent advances in sensing and tracking technology, trajectory data is becoming increasingly pervasive and analysis of trajectory data is becoming exceedingly important. A fundamental problem in analyzing trajectory data is that of identifying common patterns between pairs or among groups of trajectories. In this paper, we consider the problem of identifying similar portions between a pair of trajectories, each observed as a sequence of points sampled from it. We present new measures of trajectory similarity --- both local and global --- between a pair of trajectories to distinguish between similar and dissimilar portions. Our model is robust under noise and outliers, it does not make any assumptions on the sampling rates on either trajectory, and it works even if they are partially observed. Additionally, the model also yields a scalar similarity score which can be used to rank multiple pairs of trajectories according to similarity, e.g. in clustering applications. We also present efficient algorithms for computing the similarity under our measures; the worst-case running time is quadratic in the number of sample points. Finally, we present an extensive experimental study evaluating the effectiveness of our approach on real datasets, comparing with it with earlier approaches, and illustrating many issues that arise in trajectory data. Our experiments show that our approach is highly accurate in distinguishing similar and dissimilar portions as compared to earlier methods even with sparse sampling

Crossing the Logarithmic Barrier for Dynamic Boolean Data Structure Lower Bounds

This paper proves the first super-logarithmic lower bounds on the cell probe complexity of dynamic boolean (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds. We introduce a new method for proving dynamic cell probe lower bounds and use it to prove a $\tilde{\Omega}(\log^{1.5} n)$ lower bound on the operational time of a wide range of boolean data structure problems, most notably, on the query time of dynamic range counting over $\mathbb{F}_2$ ([Pat07]). Proving an $\omega(\lg n)$ lower bound for this problem was explicitly posed as one of five important open problems in the late Mihai P\v{a}tra\c{s}cu's obituary [Tho13]. This result also implies the first $\omega(\lg n)$ lower bound for the classical 2D range counting problem, one of the most fundamental data structure problems in computational geometry and spatial databases. We derive similar lower bounds for boolean versions of dynamic polynomial evaluation and 2D rectangle stabbing, and for the (non-boolean) problems of range selection and range median. Our technical centerpiece is a new way of "weakly" simulating dynamic data structures using efficient one-way communication protocols with small advantage over random guessing. This simulation involves a surprising excursion to low-degree (Chebychev) polynomials which may be of independent interest, and offers an entirely new algorithmic angle on the "cell sampling" method of Panigrahy et al. [PTW10]

DC field induced enhancement and inhibition of spontaneous emission in a cavity

We demonstrate how spontaneous emission in a cavity can be controlled by the application of a dc field. The method is specially suitable for Rydberg atoms. We present a simple argument for the control of emission.Comment: 3-pages, 2figure. accepted in Phys. Rev.