Measurement of Holmium Rydberg series through MOT depletion spectroscopy

We report measurements of the absolute excitation frequencies of $^{165}$Ho $4f^{11}6sns$ and $4f^{11}6snd$ odd-parity Rydberg series. The states are detected through depletion of a magneto-optical trap via a two-photon excitation scheme. Measurements of 162 Rydberg levels in the range $n=40-101$ yield quantum defects well described by the Rydberg-Ritz formula. We observe a strong perturbation in the $ns$ series around $n=51$ due to an unidentified interloper at 48515.47(4) cm$^{-1}$. From the series convergence, we determine the first ionization potential $E_\mathrm{IP}=48565.939(4)$ cm$^{-1}$, which is three orders of magnitude more accurate than previous work. This work represents the first time such spectroscopy has been done in Holmium and is an important step towards using Ho atoms for collective encoding of a quantum register.Comment: 6 figure

Determinantal Correlations of Brownian Paths in the Plane with Nonintersection Condition on their Loop-Erased Parts

As an image of the many-to-one map of loop-erasing operation \LE of random walks, a self-avoiding walk (SAW) is obtained. The loop-erased random walk (LERW) model is the statistical ensemble of SAWs such that the weight of each SAW $\zeta$ is given by the total weight of all random walks $\pi$ which are inverse images of $\zeta$, \{\pi: \LE(\pi)=\zeta \}. We regard the Brownian paths as the continuum limits of random walks and consider the statistical ensemble of loop-erased Brownian paths (LEBPs) as the continuum limits of the LERW model. Following the theory of Fomin on nonintersecting LERWs, we introduce a nonintersecting system of $N$-tuples of LEBPs in a domain $D$ in the complex plane, where the total weight of nonintersecting LEBPs is given by Fomin's determinant of an $N \times N$ matrix whose entries are boundary Poisson kernels in $D$. We set a sequence of chambers in a planar domain and observe the first passage points at which $N$ Brownian paths $(\gamma_1,..., \gamma_N)$ first enter each chamber, under the condition that the loop-erased parts (\LE(\gamma_1),..., \LE(\gamma_N)) make a system of nonintersecting LEBPs in the domain in the sense of Fomin. We prove that the correlation functions of first passage points of the Brownian paths of the present system are generally given by determinants specified by a continuous function called the correlation kernel. The correlation kernel is of Eynard-Mehta type, which has appeared in two-matrix models and time-dependent matrix models studied in random matrix theory. Conformal covariance of correlation functions is demonstrated.Comment: v3: REVTeX4, 27 pages, 10 figures, corrections made for publication in Phys.Rev.

Emergent gauge dynamics of highly frustrated magnets

Condensed matter exhibits a wide variety of exotic emergent phenomena such as the fractional quantum Hall effect and the low temperature cooperative behavior of highly frustrated magnets. I consider the classical Hamiltonian dynamics of spins of the latter phenomena using a method introduced by Dirac in the 1950s by assuming they are constrained to their lowest energy configurations as a simplifying measure. Focusing on the kagome antiferromagnet as an example, I find it is a gauge system with topological dynamics and non-locally connected edge states for certain open boundary conditions similar to doubled Chern-Simons electrodynamics expected of a $Z_2$ spin liquid. These dynamics are also similar to electrons in the fractional quantum Hall effect. The classical theory presented here is a first step towards a controlled semi-classical description of the spin liquid phases of many pyrochlore and kagome antiferromagnets and towards a description of the low energy classical dynamics of the corresponding unconstrained Heisenberg models.Comment: Updated with some appendices moved to the main body of the paper and some additional improvements. 21 pages, 5 figure

Stochastic evolutions in superspace and superconformal field theory

Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss how this may be extended to superconformal maps of N=1 superspace with links to superconformal field theory and singular vectors of the N=1 superconformal algebra in the Neveu-Schwarz sector.Comment: 13 pages, LaTe

Consequences of a Distant Massive Planet on the Large Semi-major Axis Trans-Neptunian Objects

We explore the distant giant planet hypothesis by integrating the large semi-major axis, large pericenter Trans-Neptunian Objects (TNOs) in the presence of the giant planets and an external perturber whose orbit is consistent with the proposed distant, eccentric, and inclined giant planet, so called planet 9. We find that TNOs with semi-major axes greater than 250 au experience some longitude of perihelion shepherding, but that a generic outcome of such evolutions is that the TNOs evolve to larger pericenter orbits, and commonly get raised to retrograde inclinations. This pericenter and inclination evolution requires a massive disk of TNOs (tens of M_\Earth) in order to explain the detection of the known sample today. Some of the highly inclined orbits produced by the examined perturbers will be inside of the orbital parameter space probed by prior surveys, implying a missing signature of the 9th planet scenario. The distant giant planet scenarios explored in this work do not reproduce the observed signal of simultaneous clustering in argument of pericenter, longitude of the ascending node, and longitude of perihelion in the region of the known TNOs

The mid-infrared spectrum of the transiting exoplanet HD 209458b

We report the spectroscopic detection of mid-infrared emission from the transiting exoplanet HD 209458b. Using archive data taken with the Spitzer/IRS instrument, we have determined the spectrum of HD 209458b between 7.46 and 15.25 microns. We have used two independent methods to determine the planet spectrum, one differential in wavelength and one absolute, and find the results are in good agreement. Over much of this spectral range, the planet spectrum is consistent with featureless thermal emission. Between 7.5 and 8.5 microns, we find evidence for an unidentified spectral feature. If this spectral modulation is due to absorption, it implies that the dayside vertical temperature profile of the planetary atmosphere is not entirely isothermal. Using the IRS data, we have determined the broad-band eclipse depth to be 0.00315 +/- 0.000315, implying significant redistribution of heat from the dayside to the nightside. This work required development of improved methods for Spitzer/IRS data calibration that increase the achievable absolute calibration precision and dynamic range for observations of bright point sources.Comment: 35 pages, 12 figures, revised version accepted by the Astrophysical Journa

Transforming fixed-length self-avoiding walks into radial SLE_8/3

We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial SLE with kappa=8/3 in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and then apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial SLE. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial SLE, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values

Lifetimes, transition probabilities, and level energies in Fe I

We use time-resolved laser-induced fluorescence to measure the lifetime of 186 Fe levels with energies between 25 900 and 60 758 cm . Measured emission branching fractions for these levels yield transition probabilities for 1174 transitions in the range 225-2666 nm. We find another 640 Fe transition probabilities by interpolating level populations in the inductively coupled plasma spectral source. We demonstrate the reliability of the interpolation method by comparing our transition probabilities with absorption oscillator strengths measured by the Oxford group [Blackwell et al., Mon. Not. R. Astron. Soc. 201, 595-602 (1982)]. We derive precise Fe level energies to support the automated method that is used to identify transitions in our spectra

Improved V II log(gfgf) Values, Hyperfine Structure Constants, and Abundance Determinations in the Photospheres of the Sun and Metal-poor Star HD 84937

New experimental absolute atomic transition probabilities are reported for 203 lines of V II. Branching fractions are measured from spectra recorded using a Fourier transform spectrometer and an echelle spectrometer. The branching fractions are normalized with radiative lifetime measurements to determine the new transition probabilities. Generally good agreement is found between this work and previously reported V II transition probabilities. Use of two spectrometers, independent radiometric calibration methods, and independent data analysis routines enables a reduction in systematic uncertainties, in particular those due to optical depth errors. In addition, new hyperfine structure constants are measured for selected levels by least squares fitting line profiles in the FTS spectra. The new V II data are applied to high resolution visible and UV spectra of the Sun and metal-poor star HD 84937 to determine new, more accurate V abundances. Lines covering a range of wavelength and excitation potential are used to search for non-LTE effects. Very good agreement is found between our new solar photospheric V abundance, log {\epsilon}(V) = 3.95 from 15 V II lines, and the solar-system meteoritic value. In HD 84937, we derive [V/H] = -2.08 from 68 lines, leading to a value of [V/Fe] = 0.24.Comment: 32 pages, 7 tables (3 machine-readable), 8 figures; accepted for publication in ApJ