Analysis of the entanglement between two individual atoms using global Raman rotations

Making use of the Rydberg blockade, we generate entanglement between two atoms individually trapped in two optical tweezers. In this paper we detail the analysis of the data and show that we can determine the amount of entanglement between the atoms in the presence of atom losses during the entangling sequence. Our model takes into account states outside the qubit basis and allows us to perform a partial reconstruction of the density matrix describing the two atom state. With this method we extract the amount of entanglement between pairs of atoms still trapped after the entangling sequence and measure the fidelity with respect to the expected Bell state. We find a fidelity $F_{\rm pairs} =0.74(7)$ for the 62% of atom pairs remaining in the traps at the end of the entangling sequence

Entanglement of two individual neutral atoms using Rydberg blockade

We report the generation of entanglement between two individual $^{87}$Rb atoms in hyperfine ground states $|F=1,M=1>$ and $|F=2,M=2>$ which are held in two optical tweezers separated by 4 $\mu$m. Our scheme relies on the Rydberg blockade effect which prevents the simultaneous excitation of the two atoms to a Rydberg state. The entangled state is generated in about 200 ns using pulsed two-photon excitation. We quantify the entanglement by applying global Raman rotations on both atoms. We measure that 61% of the initial pairs of atoms are still present at the end of the entangling sequence. These pairs are in the target entangled state with a fidelity of 0.75.Comment: text revised, with additional reference

Entanglement of two individual atoms using the Rydberg blockade

We report on our recent progress on the manipulation of single rubidium atoms trapped in optical tweezers and the generation of entanglement between two atoms, each individually trapped in neighboring tweezers. To create an entangled state of two atoms in their ground states, we make use of the Rydberg blockade mechanism. The degree of entanglement is measured using global rotations of the internal states of both atoms. Such internal state rotations on a single atom are demonstrated with a high fidelity.Comment: Proceeding of the 19th International Conference on Laser Spectroscopy ICOLS 2009, 7-13 June 2009, Hokkaido, Japa

Reference-based analysis of lung single-cell sequencing reveals a transitional profibrotic macrophage.

Tissue fibrosis is a major cause of mortality that results from the deposition of matrix proteins by an activated mesenchyme. Macrophages accumulate in fibrosis, but the role of specific subgroups in supporting fibrogenesis has not been investigated in vivo. Here, we used single-cell RNA sequencing (scRNA-seq) to characterize the heterogeneity of macrophages in bleomycin-induced lung fibrosis in mice. A novel computational framework for the annotation of scRNA-seq by reference to bulk transcriptomes (SingleR) enabled the subclustering of macrophages and revealed a disease-associated subgroup with a transitional gene expression profile intermediate between monocyte-derived and alveolar macrophages. These CX3CR1+SiglecF+ transitional macrophages localized to the fibrotic niche and had a profibrotic effect in vivo. Human orthologs of genes expressed by the transitional macrophages were upregulated in samples from patients with idiopathic pulmonary fibrosis. Thus, we have identified a pathological subgroup of transitional macrophages that are required for the fibrotic response to injury

E2 properties of nuclei far from stability and the proton-halo problem of 8B

E2 properties of A=6--10 nuclei, including those of nuclei far from stability, are studied by a $(0+2)\hbar\omega$ shell-model calculation which includes E2 core-polarization effects explicitly. The quadrupole moments and the E2 transition strengths in A=6--10 nuclei are described quite well by the present calculation. This result indicates that the relatively large value of the quadrupole moment of $^8$B can be understood without introducing the proton-halo in $^8$B. An interesting effect of the $2\hbar\omega$ core-polarization is found for effective charges used in the $0\hbar\omega$ shell model; although isoscalar effective-charges are almost constant as a function of nucleus, appreciable variations are needed for isovector effective-charges which play important roles in nuclei with high isospin-values.Comment: (LaTeX, 23 pages

The Gelfand spectrum of a noncommutative C*-algebra: a topos-theoretic approach

We compare two influential ways of defining a generalized notion of space. The first, inspired by Gelfand duality, states that the category of 'noncommutative spaces' is the opposite of the category of C*-algebras. The second, loosely generalizing Stone duality, maintains that the category of 'pointfree spaces' is the opposite of the category of frames (i.e., complete lattices in which the meet distributes over arbitrary joins). One possible relationship between these two notions of space was unearthed by Banaschewski and Mulvey, who proved a constructive version of Gelfand duality in which the Gelfand spectrum of a commutative C*-algebra comes out as a pointfree space. Being constructive, this result applies in arbitrary toposes (with natural numbers objects, so that internal C*-algebras can be defined). Earlier work by the first three authors, shows how a noncommutative C*-algebra gives rise to a commutative one internal to a certain sheaf topos. The latter, then, has a constructive Gelfand spectrum, also internal to the topos in question. After a brief review of this work, we compute the so-called external description of this internal spectrum, which in principle is a fibered pointfree space in the familiar topos Sets of sets and functions. However, we obtain the external spectrum as a fibered topological space in the usual sense. This leads to an explicit Gelfand transform, as well as to a topological reinterpretation of the Kochen-Specker Theorem of quantum mechanics, which supplements the remarkable topos-theoretic version of this theorem due to Butterfield and Isham.Comment: 12 page

Improved EEG source localization with Bayesian uncertainty modelling of unknown skull conductivity

Electroencephalography (EEG) source imaging is an ill-posed inverse problem that requires accurate conductivity modelling of the head tissues, especially the skull. Unfortunately, the conductivity values are difficult to determine in vivo. In this paper, we show that the exact knowledge of the skull conductivity is not always necessary when the Bayesian approximation error (BAE) approach is exploited. In BAE, we first postulate a probability distribution for the skull conductivity that describes our (lack of) knowledge on its value, and model the effects of this uncertainty on EEG recordings with the help of an additive error term in the observation model. Before the Bayesian inference, the likelihood is marginalized over this error term. Thus, in the inversion we estimate only our primary unknown, the source distribution. We quantified the improvements in the source localization when the proposed Bayesian modelling was used in the presence of different skull conductivity errors and levels of measurement noise. Based on the results, BAE was able to improve the source localization accuracy, particularly when the unknown (true) skull conductivity was much lower than the expected standard conductivity value. The source locations that gained the highest improvements were shallow and originally exhibited the largest localization errors. In our case study, the benefits of BAE became negligible when the signal-to-noise ratio dropped to 20 dB.</p