22,672 research outputs found

    An invitation to quantum tomography (II)

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    The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which the state is the unknown parameter and the data is given by results of measurements performed on identical quantum systems. We present consistency results for Pattern Function Projection Estimators as well as for Sieve Maximum Likelihood Estimators for both the density matrix of the quantum state and its Wigner function. Finally we illustrate via simulated data the performance of the estimators. An EM algorithm is proposed for practical implementation. There remain many open problems, e.g. rates of convergence, adaptation, studying other estimators, etc., and a main purpose of the paper is to bring these to the attention of the statistical community.Comment: An earlier version of this paper with more mathematical background but less applied statistical content can be found on arXiv as quant-ph/0303020. An electronic version of the paper with high resolution figures (postscript instead of bitmaps) is available from the authors. v2: added cross-validation results, reference

    Deterministic entanglement of two neutral atoms via Rydberg blockade

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    We demonstrate the first deterministic entanglement of two individually addressed neutral atoms using a Rydberg blockade mediated controlled-NOT gate. Parity oscillation measurements reveal an entanglement fidelity of F=0.58±0.04F=0.58\pm0.04, which is above the entanglement threshold of F=0.5F=0.5, without any correction for atom loss, and F=0.71±0.05F=0.71\pm0.05 after correcting for background collisional losses. The fidelity results are shown to be in good agreement with a detailed error model.Comment: 4 figure

    Technology evaluation of heating, ventilation, and air conditioning for MIUS application

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    Potential ways of providing heating, ventilation, and air conditioning for a building complex serviced by a modular integrated utility system (MIUS) are examined. Literature surveys were conducted to investigate both conventional and unusual systems to serve this purpose. The advantages and disadvantages of the systems most compatible with MIUS are discussed

    Uniform electron gases: III. Low-density gases on three-dimensional spheres

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    By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e.~the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems, and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e. the minimum-energy arrangement of nn point charges) on the 3-sphere for various values of nn. We have found 11 special values of nn whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids --- the hyper-tetrahedron (n=5n=5), the hyper-octahedron (n=8n=8) and the 24-cell (n=24n=24) --- and a fourth is a highly symmetric structure (n=13n=13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.Comment: 6 pages, 2 figures, accepted for publication in the Journal of Chemical Physic

    Analytical and structural studies of acacia polysaccharides

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    An analytical study of eleven Acacia gums from the subseries Juliflorae of the series Phyllodineae showed them to be more proteinaceous, more acidic and more viscous, with higher methoxyl contents and higher molecular weights but with lower proportions of rhamnose and arabinose than the majority of Acacia gums studied so far.A structural study of the gum from Acacia auriculiformis involving hydrolysis, Smith- degradation and methylation studies, revealed a ß -1, 3 - linked galactose backbone with side chains of ß -1, 6 - linked galactose. Glucuronic acid was present as end-groups, linked ß-1, 6 to galactose: 4-Ω-methyl glucuronic acid was present as end - groups, α -1, 4 - linked to galactose. Arabinose was present in short, ß-1, 3- linked chains, while rhamnose was present as end-group. Proteinaceous material was attached to the molecule by periodate- resistant linkages.The use of carbon 13-nuclear magnetic resonance spectroscopy for the study of gum exudates was examined. Spectra were obtained for the gum from Acacia auriculiformis and its degradation products, despite their high molecular weight and chemical complexity. The spectra substantiated the findings of the structural study

    Analytic Representation of The Dirac Equation

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    In this paper we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the wave functions, as is done by the Foldy-Wouthuysen method, and reveals the nonlocal time behavior of the particle-antiparticle relationship. We interpret the zitterbewegung and the result that a velocity measurement (of a Dirac particle) at any instant in time is, as reflections of the fact that the Dirac equation makes a spatially extended particle appear as a point in the present by forcing it to oscillate between the past and future at speed c. From this we infer that, although the form of the Dirac equation serves to make space and time appear on an equal footing mathematically, it is clear that they are still not on an equal footing from a physical point of view. On the other hand, the Foldy-Wouthuysen transformation, which connects the Dirac and square root operator, is unitary. Reflection on these results suggests that a more refined notion (than that of unitary equivalence) may be required for physical systems

    Solid-state electronic spin coherence time approaching one second

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    Solid-state electronic spin systems such as nitrogen-vacancy (NV) color centers in diamond are promising for applications of quantum information, sensing, and metrology. However, a key challenge for such solid-state systems is to realize a spin coherence time that is much longer than the time for quantum spin manipulation protocols. Here we demonstrate an improvement of more than two orders of magnitude in the spin coherence time (T2T_2) of NV centers compared to previous measurements: T2≈0.5T_2 \approx 0.5 s at 77 K, which enables ∼107\sim 10^7 coherent NV spin manipulations before decoherence. We employed dynamical decoupling pulse sequences to suppress NV spin decoherence due to magnetic noise, and found that T2T_2 is limited to approximately half of the longitudinal spin relaxation time (T1T_1) over a wide range of temperatures, which we attribute to phonon-induced decoherence. Our results apply to ensembles of NV spins and do not depend on the optimal choice of a specific NV, which could advance quantum sensing, enable squeezing and many-body entanglement in solid-state spin ensembles, and open a path to simulating a wide range of driven, interaction-dominated quantum many-body Hamiltonians
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