Bringing closure to microlensing mass measurement

Interferometers offer multiple methods for studying microlensing events and determining the properties of the lenses. We investigate the study of microlensing events with optical interferometers, focusing on narrow-angle astrometry, visibility, and closure phase. After introducing the basics of microlensing and interferometry, we derive expressions for the signals in each of these three channels. For various forecasts of the instrumental performance, we discuss which method provides the best means of measuring the lens angular Einstein radius theta_E, a prerequisite for determining the lens mass. If the upcoming generation of large-aperture, AO-corrected long baseline interferometers (e.g. VLTI, Keck, OHANA) perform as well as expected, theta_E may be determined with signal-to-noise greater than 10 for all bright events. We estimate that roughly a dozen events per year will be sufficiciently bright and have long enough durations to allow the measurement of the lens mass and distance from the ground. We also consider the prospects for a VLTI survey of all bright lensing events using a Fisher matrix analysis, and find that even without individual masses, interesting constraints may be placed on the bulge mass function, although large numbers of events would be required.Comment: 23 pages, aastex, submitted to Ap

Influence of vector interactions on the hadron-quark/gluon phase transition

The hadron-quark/gluon phase transition is studied in the two-phase model. As a further study of our previous work, both the isoscalar and isovector vector interactions are included in the Polyakov loop modified Nambu--Jona-Lasinio model (PNJL) for the quark phase. The relevance of the exchange (Fock) terms is stressed and suitably accounted for. The calculation shows that the isovector vector interaction delays the phase transition to higher densities and the range of the mixed phase correspondingly shrinks. Meanwhile the asymmetry parameter of quark matter in the mixed phase decreases with the strengthening of this interaction channel. This leads to some possible observation signals being weakened, although still present. We show that these can be rather general effects of a repulsion in the quark phase due to the symmetry energy. This is also confirmed by a simpler calculation with the MIT--Bag model. However, the asymmetry parameter of quark matter is slightly enhanced with the inclusion of the isoscalar vector interaction, but the phase transition will be moved to higher densities. The largest uncertainty on the phase transition lies in the undetermined coupling constants of the vector interactions. In this respect new data on the mixed phase obtained from Heavy Ion Collisions at Intermediate Energies appear very important.Comment: submitted to Phys. Rev.

Entanglement entropy of the ν=1/2\nu=1/2 composite fermion non-Fermi liquid state

The so-called ``non-Fermi liquid'' behavior is very common in strongly correlated systems. However, its operational definition in terms of ``what it is not'' is a major obstacle against theoretical understanding of this fascinating correlated state. Recently there has been much interest in entanglement entropy as a theoretical tool to study non-Fermi liquids. So far explicit calculations have been limited to models without direct experimental realizations. Here we focus on a two dimensional electron fluid under magnetic field and filling fraction $\nu=1/2$, which is believed to be a non-Fermi liquid state. Using the composite fermion (CF) wave-function which captures the $\nu=1/2$ state very accurately, we compute the second R\'enyi entropy using variational Monte-Carlo technique and an efficient parallel algorithm. We find the entanglement entropy scales as $L\log L$ with the length of the boundary $L$ as it does for free fermions, albeit with a pre-factor twice that of the free fermion. We contrast the results against theoretical conjectures and discuss the implications of the results.Comment: 4+ page

The Palomar Testbed Interferometer

The Palomar Testbed Interferometer (PTI) is a long-baseline infrared interferometer located at Palomar Observatory, California. It was built as a testbed for interferometric techniques applicable to the Keck Interferometer. First fringes were obtained in July 1995. PTI implements a dual-star architecture, tracking two stars simultaneously for phase referencing and narrow-angle astrometry. The three fixed 40-cm apertures can be combined pair-wise to provide baselines to 110 m. The interferometer actively tracks the white-light fringe using an array detector at 2.2 um and active delay lines with a range of +/- 38 m. Laser metrology of the delay lines allows for servo control, and laser metrology of the complete optical path enables narrow-angle astrometric measurements. The instrument is highly automated, using a multiprocessing computer system for instrument control and sequencing.Comment: ApJ in Press (Jan 99) Fig 1 available from http://huey.jpl.nasa.gov/~bode/ptiPicture.html, revised duging copy edi

Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid

We propose an experiment to directly probe the non-Abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana bound states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark state subspace.Comment: 4 pages; Add detailed discussion of feasibility of the scheme;add ref

The PHASES Differential Astrometry Data Archive. I. Measurements and Description

The Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES) monitored 51 sub-arcsecond binary systems to determine precision binary orbits, study the geometries of triple and quadruple star systems, and discover previously unknown faint astrometric companions as small as giant planets. PHASES measurements made with the Palomar Testbed Interferometer (PTI) from 2002 until PTI ceased normal operations in late 2008 are presented. Infrared differential photometry of several PHASES targets were measured with Keck Adaptive Optics and are presented.Comment: 33 pages emulateapj, Accepted to A

Perceptual learning of dot pattern

Dot pattern is a type of pattern defined by specific spatial relationship among some dots. As a compensation for concrete and meaningful visual stimuli, meaningless dot pattern can be used as stimuli in learning tasks. We performed an experiment for exploring the perceptual learning process of dot pattern against random-dot background. Participants were required to learn two types of dot patterns (9-dot and 11-dot). They were assigned to two groups: participants in Group 1 learned 9-dot pattern first and 11-dot pattern later, while those in Group 2 learned 11-dot pattern first and 9-dot pattern later. The results showed that participants could acquire the spatial relationship of dot pattern through perceptual learning in relatively short learning time. In comparison with 9-dot pattern, learning time of 11-dot pattern was slightly longer and its accuracy rate lower, but there was significant positive transfer effect from 11-dot pattern learning to 9-dot learning

Bell Inequalities Classifying Bi-separable Three-qubit States

We present a set of Bell inequalities that gives rise to a finer classification of the entanglement for tripartite systems. These inequalities distinguish three possible bi-separable entanglements for three-qubit states. The three Bell operators we employed constitute an external sphere of the separable cube.Comment: 8 page

Masses, luminosities, and orbital coplanarities of the µ Orionis quadruple-star system from phases differential astrometry

μ Orionis was identified by spectroscopic studies as a quadruple-star system. Seventeen high-precision differential astrometry measurements of μ Ori have been collected by the Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES). These show both the motion of the long-period binary orbit and short-period perturbations superimposed on that caused by each of the components in the long-period system being themselves binaries. The new measurements enable the orientations of the long-period binary and short-period subsystems to be determined. Recent theoretical work predicts the distribution of relative inclinations between inner and outer orbits of hierarchical systems to peak near 40 and 140 degrees. The degree of coplanarity of this complex system is determined, and the angle between the planes of the A–B and Aa–Ab orbits is found to be 136.7 ± 8.3 degrees, near the predicted distribution peak at 140 degrees; this result is discussed in the context of the handful of systems with established mutual inclinations. The system distance and masses for each component are obtained from a combined fit of the PHASES astrometry and archival radial velocity observations. The component masses have relative precisions of 5% (component Aa), 15% (Ab), and 1.4% (each of Ba and Bb). The median size of the minor axes of the uncertainty ellipses for the new measurements is 20 micro-arcseconds (μas). Updated orbits for δ Equulei, κ Pegasi, and V819 Herculis are also presented