A Natural Formalism for Microlensing

If the standard microlensing geometry is inverted so that the Einstein ring is projected onto the observer plane rather than the source plane, then the relations between the observables (\theta_E,\tilde r_E) and the underlying physical quantities (M,\pi_rel) become immediately obvious. Here \theta_E and \tilde r_E are the angular and projected Einstein radii, M is the mass of the lens, and \pi_rel is the lens-source relative parallax. I recast the basic formalism of microlensing in light of this more natural geometry and in terms of observables. I then find that the relations between observable and physical quantities assume an exceptionally simple form. In an appendix, I propose a set of notational conventions for microlensing.Comment: 8 pages, 1 figure tells all. Interested parties are requested to vote on a proposed standard for microlensing notation given in the appendix. Submitted to Ap

The Effect of Symmetry Lowering on the Dielectric Response of BaZrO3BaZrO_3

We use first-principles density functional theory calculations to investigate the dielectric response of BaZrO$_3$ perovskite. A previous study [Arkbarzadeh {\em et al.} Phys. Rev. B {\bf 72}, 205104 (2005)] reported a disagreement between experimental and theoretical low temperature dielectric constant $\epsilon$ for the high symmetry BaZrO$_3$ structure. We show that a fully relaxed 40-atom BaZrO$_3$ structure exhibits O$_6$ octahedral tilting, and $\epsilon$ that agrees with experiment. The change in $\epsilon$ from high-symmetry to low-symmetry structure is due to increased phonon frequencies as well as decreased mode effective charges.Comment: 4 pages, 2 figure

Microlens Parallaxes with SIRTF

The Space Infrared Telescope Facility (SIRTF) will drift away from the Earth at about 0.1 AU/yr. Microlensing events will therefore have different characteristics as seen from the satellite and the Earth. From the difference, it is possible in principle to measure v-tilde, the transverse velocity of the lens projected onto the observer plane. Since v-tilde has very different values for different populations (disk, halo, Large Magellanic Cloud), such measurements could help identify the location, and hence the nature, of the lenses. I show that the method previously developed by Gould for measuring such satellite parallaxes fails completely in the case of SIRTF: it is overwhelmed by degeneracies which arise from fact that the Earth and satellite observations are in different band passes. I develop a new method which allows for observations in different band passes and yet removes all degeneracies. The method combines a purely ground-based measurement of the "parallax asymmetry" with a measurement of the delay between the time the event peaks at the Earth and satellite. In effect, the parallax asymmetry determines the component of v-tilde in the Earth-Sun direction, while the delay time measures the component of v-tilde in the direction of the Earth's orbit.Comment: 21 pages plus 3 figure

Microlens Parallax Asymmetries Toward the LMC

If the microlensing events now being detected toward the Large Magellanic Cloud (LMC) are due to lenses in the Milky Way halo, then the events should typically have asymmetries of order 1% due to parallax from the reflex motion of the Earth. By contrast, if the lenses are in the LMC, the parallax effects should be negligible. A ground-based search for such parallax asymmetries would therefore clarify the location of the lenses. A modest effort (2 hours per night on a 1 m telescope) could measure 15 parallax asymmetries over 5 years and so marginally discriminate between the halo and the LMC as the source of the lenses. A dedicated 1 m telescope would approximately double the number of measurements and would therefore clearly distinguish between the alternatives. However, compared to satellite parallaxes, the information extracted from ground-based parallaxes is substantially less useful for understanding the nature of the halo lenses (if that is what they are). The backgrounds of asymmetries due to binary-source and binary-lens events are estimated to be approximately 7% and 12% respectively. These complicate the interpretation of detected parallax asymmetries, but not critically.Comment: Submitted to ApJ, 17 pages, including 2 embedded figure

Complete Parallax and Proper Motion Solutions For Halo Binary-Lens Microlensing Events

A major problem in the interpretation of microlensing events is that the only measured quantity, the Einstein time scale t_E, is a degenerate combination of the three quantities one would like to know, the mass, distance, and speed of the lens. This degeneracy can be partly broken by measuring either a "parallax" or a "proper motion" and completely broken by measuring both. Proper motions can easily be measured for caustic-crossing binary-lens events. Here we examine the possibility (first discussed by Hardy & Walker) that one could also measure a parallax for some of these events by comparing the light curves of the caustic crossing as seen from two observatories on Earth. We derive analytic expressions for the signal-to-noise ratio of the parallax measurement in terms of the characteristics of the source and the geometry of the event. For Galactic halo binary lenses seen toward the LMC, the light curve is delayed from one continent to another by a seemingly minuscule 15 seconds (compared to t_E ~ 40 days). However, this is sufficient to cause a difference in magnification of order 10%. To actually extract complete parallax information (as opposed to merely detecting the effect) requires observations from three non-collinear observatories. Parallaxes cannot be measured for binary lenses in the LMC but they can be measured for Galactic halo binary lenses seen toward M31. Robust measurements are possible for disk binary lenses seen toward the Galactic bulge, but are difficult for bulge binary lenses.Comment: Revised to take account of important work by Hardy & Walker (1995

Giant Stark effect in the emission of single semiconductor quantum dots

We study the quantum-confined Stark effect in single InAs/GaAs quantum dots embedded within a AlGaAs/GaAs/AlGaAs quantum well. By significantly increasing the barrier height we can observe emission from a dot at electric fields of -500 kV/cm, leading to Stark shifts of up to 25 meV. Our results suggest this technique may enable future applications that require self-assembled dots with transitions at the same energy

Quantum state restoration and single-copy tomography

Given a single copy of an n qubit quantum state |psi>, the no-cloning theorem greatly limits the amount of information which can be extracted from it. Moreover, given only a procedure which verifies the state, for example a procedure which measures the operator |psi> in time polynomial in n . In this paper, we consider the scenario in which we are given both a single copy of |psi> and the ability to verify it. We show that in this setting, we can do several novel things efficiently. We present a new algorithm that we call quantum state restoration which allows us to extend a large subsystem of |psi> to the full state, and in turn this allows us to copy small subsystems of |psi>. In addition, we present algorithms that can perform tomography on small subsystems of |psi>, and we show how to use these algorithms to estimate the statistics of any efficiently implementable POVM acting on |psi> in time polynomial in the number of outcomes of the POVM.Comment: edited for clarity; 13 pages, 1 figur

Systematic Analysis of 22 Microlensing Parallax Candidates

We attempt to identify all microlensing parallax events for which the parallax fit improves \Delta\chi^2 > 100 relative to a standard microlensing model. We outline a procedure to identify three types of discrete degeneracies (including a new one that we dub the ``ecliptic degeneracy'') and find many new degenerate solutions in 16 previously published and 6 unpublished events. Only four events have one unique solution and the other 18 events have a total of 44 solutions. Our sample includes three previously identified black-hole (BH) candidates. We consider the newly discovered degenerate solutions and determine the relative likelihood that each of these is a BH. We find the lens of event MACHO-99-BLG-22 is a strong BH candidate (78%), event MACHO-96-BLG-5 is a marginal BH candidate (37%), and MACHO-98-BLG-6 is a weak BH candidate (2.2%). The lens of event OGLE-2003-BLG-84 may be a Jupiter-mass free-floating planet candidate based on a weak 3 sigma detection of finite-source effects. We find that event MACHO-179-A is a brown dwarf candidate within ~100 pc of the Sun, mostly due to its very small projected Einstein radius, \tilde r_E = 0.23+-0.05 AU. As expected, these microlensing parallax events are biased toward lenses that are heavier and closer than average. These events were examined for xallarap (or binary-source motion), which can mimic parallax. We find that 23% of these events are strongly affected by xallarap.Comment: 69 Pages, 10 Figures, 24 Tables, Submitted to Ap