The Gradients in the 47 Tuc Red Giant Branch Bump and Horizontal Branch are Consistent With a Centrally-Concentrated, Helium-Enriched Second Stellar Generation

We combine ground and space-based photometry of the Galactic globular cluster 47 Tuc to measure four independent lines of evidence for a helium gradient in the cluster, whereby stars in the cluster outskirts would have a lower initial helium abundance than stars in and near the cluster core. First and second, we show that the red giant branch bump (RGBB) stars exhibit gradients in their number counts and brightness. With increased separation from the cluster center, they become more numerous relative to the other red giant (RG) stars. They also become fainter. For our third and fourth lines of evidence, we show that the horizontal branch (HB) of the cluster becomes both fainter and redder for sightlines farther from the cluster center. These four results are respectively detected at the 2.3$\sigma$, 3.6$\sigma$, 7.7$\sigma$ and 4.1$\sigma$ levels. Each of these independent lines of evidence is found to be significant in the cluster-outskirts; closer in, the data are more compatible with uniform mixing. Our radial profile is qualitatively consistent with but quantitatively tighter than previous results based on CN absorption. These observations are qualitatively consistent with a scenario wherein a second generation of stars with modestly enhanced helium and CNO abundance formed deep within the gravitational potential of a cluster of previous generation stars having more canonical abundances.Comment: 20 pages, 6 figures, 1 table, submitted to The Astrophysical Journa

Heisenberg Uncertainty Principle as Probe of Entanglement Entropy: Application to Superradiant Quantum Phase Transitions

Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy and one of the most fundamental and simplest measure of the quantum fluctuations, the Heisenberg uncertainty principle. Then, we show that the latter represents a sensitive probe of superradiant quantum phase transitions in standard models of photons such as the Dicke Hamiltonian, which embodies an ensemble of two-level systems interacting with one quadrature of a single and uniform bosonic field. We derive exact results in the thermodynamic limit and for a finite number N of two-level systems: as a reminiscence of the entanglement properties between light and the two-level systems, the product $\Delta x\Delta p$ diverges at the quantum critical point as $N^{1/6}$. We generalize our results to the double quadrature Dicke model where the two quadratures of the bosonic field are now coupled to two independent sets of two level systems. Our findings, which show that the entanglement properties between light and matter can be accessed through the Heisenberg uncertainty principle, can be tested using Bose-Einstein condensates in optical cavities and circuit quantum electrodynamicsComment: 7 pages, 3 figures. Published Versio

Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice

We provide numerical evidence in favor of spontaneous chiral symmetry breaking and the concomitant appearance of an Abelian chiral spin liquid for three-component fermions on the triangular lattice described by an SU(3) symmetric Hubbard model with hopping amplitude $-t$ ($t>0$) and on-site interaction $U$. This chiral phase is stabilized in the Mott phase with one particle per site in the presence of a uniform $\pi$-flux per plaquette, and in the Mott phase with two particles per site without any flux. Our approach relies on effective spin models derived in the strong-coupling limit in powers of $t/U$ for general SU$(N)$ and arbitrary uniform charge flux per plaquette, which are subsequently studied using exact diagonalizations and variational Monte Carlo simulations for $N=3$, as well as exact diagonalizations of the SU($3$) Hubbard model on small clusters. Up to third order in $t/U$, and for the time-reversal symmetric cases (flux $0$ or $\pi$), the low-energy description is given by the $J$-$K$ model with Heisenberg coupling $J$ and real ring exchange $K$. The phase diagram in the full $J$-$K$ parameter range contains, apart from three already known, magnetically long-range ordered phases, two previously unreported phases: i) a lattice nematic phase breaking the lattice rotation symmetry and ii) a spontaneous time-reversal and parity symmetry breaking Abelian chiral spin liquid. For the Hubbard model, an investigation that includes higher-order itinerancy effects supports the presence of a phase transition inside the insulating region, occurring at $(t/U)_{\rm c}\approx 0.07$ [$(U/t)_{\rm c} \approx 13$] between the three-sublattice magnetically ordered phase at small $t/U$ and this Abelian chiral spin liquid.Comment: 21 pages, 23 figure

High-contrast imaging of 180{\deg} ferroelectric domains by optical microscopy using ferroelectric liquid crystals

Ferroelectric liquid crystals (FLCs) couple the direction of their spontaneous electric polarization to the direction of tilt of their optic axis. Consequently, reversal of the electric polarization by an electric field gives rise to an immediate and lasting optical response when an appropriately aligned FLC is observed between crossed polarizers, with one field direction yielding a dark image, and the opposite direction yielding a bright image. Here this peculiar electro-optic response is used to image, with high optical contrast, 180{\deg} ferroelectric domains in a crystalline substrate of magnesium-doped lithium niobate. The lithium niobate substrate contains a few domains with upwards electric polarization surrounded by regions with downward electric polarization. In contrast to a reference non-chiral liquid crystal that is unable to show ferroelectric behavior due to its high symmetry, the FLC, which is used as a thin film confined between the lithium niobate substrate and an inert aligning substrate, reveals ferroelectric domains as well as their boundaries, with strong black and white contrast. The results show that FLCs can be used for non-destructive read-out of domains in underlying ferroelectrics, with potential applications in e.g. photonic devices and non-volatile ferroelectric memories.Comment: 12 pages, 3 figure

Optimal Survey Strategies and Predicted Planet Yields for the Korean Microlensing Telescope Network

The Korean Microlensing Telescope Network (KMTNet) will consist of three 1.6m telescopes each with a 4 deg^{2} field of view (FoV) and will be dedicated to monitoring the Galactic Bulge to detect exoplanets via gravitational microlensing. KMTNet's combination of aperture size, FoV, cadence, and longitudinal coverage will provide a unique opportunity to probe exoplanet demographics in an unbiased way. Here we present simulations that optimize the observing strategy for, and predict the planetary yields of, KMTNet. We find preferences for four target fields located in the central Bulge and an exposure time of t_{exp} = 120s, leading to the detection of ~2,200 microlensing events per year. We estimate the planet detection rates for planets with mass and separation across the ranges 0.1 <= M_{p}/M_{Earth} <= 1000 and 0.4 <= a/AU <= 16, respectively. Normalizing these rates to the cool-planet mass function of Cassan (2012), we predict KMTNet will be approximately uniformly sensitive to planets with mass 5 <= M_{p}/M_{Earth} <= 1000 and will detect ~20 planets per year per dex in mass across that range. For lower-mass planets with mass 0.1 <= M_{p}/M_{Earth} < 5, we predict KMTNet will detect ~10 planets per year. We also compute the yields KMTNet will obtain for free-floating planets (FFPs) and predict KMTNet will detect ~1 Earth-mass FFP per year, assuming an underlying population of one such planet per star in the Galaxy. Lastly, we investigate the dependence of these detection rates on the number of observatories, the photometric precision limit, and optimistic assumptions regarding seeing, throughput, and flux measurement uncertainties.Comment: 29 pages, 31 figures, submitted to ApJ. For a brief video explaining the key results of this paper, please visit: https://www.youtube.com/watch?v=e5rWVjiO26

Protected quantum computation with multiple resonators in ultrastrong coupling circuit QED

We investigate theoretically the dynamical behavior of a qubit obtained with the two ground eigenstates of an ultrastrong coupling circuit-QED system consisting of a finite number of Josephson fluxonium atoms inductively coupled to a transmission line resonator. We show an universal set of quantum gates by using multiple transmission line resonators (each resonator represents a single qubit). We discuss the intrinsic 'anisotropic' nature of noise sources for fluxonium artificial atoms. Through a master equation treatment with colored noise and manylevel dynamics, we prove that, for a general class of anisotropic noise sources, the coherence time of the qubit and the fidelity of the quantum operations can be dramatically improved in an optimal regime of ultrastrong coupling, where the ground state is an entangled photonic 'cat' state.Comment: Added results with N = 3,4,5 Josephson atoms and different anisotropy ratios for the decoherence channels in the new figures 2 and

Magnetic properties of the honeycomb oxide Na2_2Co2_2TeO6_6

We have studied the magnetic properties of Na$_2$Co$_2$TeO$_6$, which features a honeycomb lattice of magnetic Co$^{2+}$ ions, through macroscopic characterization and neutron diffraction on a powder sample. We have shown that this material orders in a zig-zag antiferromagnetic structure. In addition to allowing a linear magnetoelectric coupling, this magnetic arrangement displays very peculiar spatial magnetic correlations, larger in the honeycomb planes than between the planes, which do not evolve with the temperature. We have investigated this behavior by Monte Carlo calculations using the $J_1$-$J_2$-$J_3$ model on a honeycomb lattice with a small interplane interaction. Our model reproduces the experimental neutron structure factor, although its absence of temperature evolution must be due to additional ingredients, such as chemical disorder or quantum fluctuations enhanced by the proximity to a phase boundary.Comment: 9 pages, 13 figure

Red Giant Branch Bump Brightness and Number Counts in 72 Galactic Globular Clusters Observed with the Hubble Space Telescope

We present the broadest and most precise empirical investigation of red giant branch bump (RGBB) brightness and number counts ever conducted. We implement a new method and use data from two \textit{Hubble Space Telescope (HST)} globular cluster (GC) surveys to measure the brightness and star counts of the RGBB in 72 GCs. The brightness is measured to a precision better than 0.01 mag while the precision in number counts reaches 10%. The position of the main-sequence turnoff (MSTO) and the number of horizontal branch (HB) stars are used as comparisons where appropriate. Several independent scientific conclusions are newly possible with our parametrization of the RGBB. Both brightness and number counts are shown to have second parameters in addition to their strong dependence on metallicity. The RGBBs are found to be anomalous in the GCs NGC 2808, 5286, 6388 and 6441, likely due to the presence of multiple populations. Finally, we use our empirical calibration to predict the properties of the Galactic bulge RGBB if the assumption of similar stellar physics for the bulge and Galactic GC system holds. The RGBB properties for the bulge are shown to differ from those of the Galactic GC system, with the former having lower number counts, a lower brightness dispersion and a brighter peak luminosity than would be expected from the latter. This discrepancy is well explained by the Galactic bulge having a higher helium abundance than expected from GCs, ${\Delta}$Y$\sim +$0.06 at the median metallicity.Comment: 66 pages, 21 figures, 7 tables, Accepted for publication in The Astrophysical Journal, modified following referee repor

Experimental study of super-rotation in a magnetostrophic spherical Couette flow

We report measurements of electric potentials at the surface of a spherical container of liquid sodium in which a magnetized inner core is differentially rotating. The azimuthal angular velocities inferred from these potentials reveal a strong super-rotation of the liquid sodium in the equatorial region, for small differential rotation. Super-rotation was observed in numerical simulations by Dormy et al. [1]. We find that the latitudinal variation of the electric potentials in our experiments differs markedly from the predictions of a similar numerical model, suggesting that some of the assumptions used in the model - steadiness, equatorial symmetry, and linear treatment for the evolution of both the magnetic and velocity fields - are violated in the experiments. In addition, radial velocity measurements, using ultrasonic Doppler velocimetry, provide evidence of oscillatory motion near the outer sphere at low latitude: it is viewed as the signature of an instability of the super-rotating region

Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property