Leggett-Garg inequalities and the geometry of the cut polytope

The Bell and Leggett-Garg tests offer operational ways to demonstrate that non-classical behavior manifests itself in quantum systems, and experimentalists have implemented these protocols to show that classical worldviews such as local realism and macrorealism are false, respectively. Previous theoretical research has exposed important connections between more general Bell inequalities and polyhedral combinatorics. We show here that general Leggett-Garg inequalities are closely related to the cut polytope of the complete graph, a geometric object well-studied in combinatorics. Building on that connection, we offer a family of Leggett-Garg inequalities that are not trivial combinations of the most basic Leggett-Garg inequalities. We then show that violations of macrorealism can occur in surprising ways, by giving an example of a quantum system that violates the new "pentagon" Leggett-Garg inequality but does not violate any of the basic "triangle" Leggett-Garg inequalities.Comment: 5 pages, 1 figur

Spin gradient thermometry for ultracold atoms in optical lattices

We demonstrate spin gradient thermometry, a new general method of measuring the temperature of ultracold atoms in optical lattices. We realize a mixture of spins separated by a magnetic field gradient. Measurement of the width of the transition layer between the two spin domains serves as a new method of thermometry which is observed to work over a broad range of lattice depths and temperatures, including in the Mott insulator regime. We demonstrate the thermometry in a system of ultracold rubidium atoms, and suggest that interesting spin physics can be realized in this system. The lowest measured temperature is 1 nK, indicating that the system has reached the quantum regime, where insulating shells are separated by superfluid layers.Comment: 5 pages, 3 figures, minor edits for clarit

Thermometry and Refrigeration in a Two-Component Mott Insulator of Ultracold Atoms

Interesting spin Hamiltonians can be realized with ultracold atoms in a two-component Mott insulator (2CMI). It was recently demonstrated that the application of a magnetic field gradient to the 2CMI enables new techniques of thermometry and adiabatic cooling. Here we present a theoretical description which provides quantitative analysis of these two new techniques. We show that adiabatic reduction of the field gradient is capable of cooling below the Curie or N\'eel temperature of certain spin ordered phases.Comment: 5 pages, 5 figures (v4): Added journal referenc

WETLAND OCCUPANCY OF POND-BREEDING AMPHIBIANS IN YOSEMITE NATIONAL PARK, USA

We estimated wetland occupancy and population trends for three species of pond-breeding anurans in Yosemite National Park from 2007 – 2011. We used a double survey technique in which two observers independently surveyed each site on the same day. Double surveys allowed us to calculate detectability for the three most common anurans within the park: Rana sierrae, Anaxyrus canorus, and Pseudacris regilla. Annual estimates of detectability were generally high; mean detectability ranged from 73.7% + 0.6 (SE) for any life history stage of A. canorus to 86.7% + 0.7 for sites with P. regilla reproduction (eggs or larvae present). Detectability was most variable for Anaxyrus canorus, which ranged from 45.9% to 99.7%. The probability of occupancy for R. sierrae was highest in larger, low-elevation wetlands that lacked fish. Anaxyrus canorus were more common in shallow high-elevation ponds; their occurrence was minimally impacted by the presence of fish. Finally, occurrence of P. regilla was largely unrelated to wetland size and elevation, but like R. sierrae, they were less likely to occupy sites with fish. Occupancy showed no trend over the five years of our study for R. sierrae or A. canorus when considering either sites with any life stage or only sites with reproduction. However, P. regilla showed a modest downward trend for sites with any life stage and sites with reproduction. Our results for R. sierrae run counter to expectations given recent concern about the decline of this species, while our findings for P. regilla raise concerns for this widespread and generally common species

Cirrus cloud properties derived from coincident GOES and lidar data during the 1986 FIRE Cirrus Intensive Field Observations (IFO)

One of the main difficulties in detecting cirrus clouds and determining their correct altitude using satellite measurements is their nonblackness. In the present algorithm (Rossow et al., 1985) used by the International Satellite Cloud Climatology Project (ISCCP), the cirrus cloud emissivity is estimated from the derived cloud reflectance using a theoretical model relating visible (VIS, 0.65 micron) optical depth to infrared (IR, 10.5 micron) emissivity. At this time, it is unknown how accurate this approach is or how the derived cloud altitude relates to the physical properties of the cloud. The First ISCCP Regional Experiment (FIRE) presents opportunities for determining how the observed radiances depend on the cloud properties. During the FIRE Cirrus Intensive Field Observations (IFO, see Starr, 1987), time series of cloud thickness, height, and relative optical densities were measured from several surface-based lidars. Cloud microphysics and radiances at various wavelengths were also measured simultaneously over these sites from aircraft at specific times during the IFO (October 19 to November 2, 1986). Satellite-observed radiances taken simultaneously can be matched with these data to determine their relationships to the cirrus characteristics. The first step is taken toward relating all of these variables to the satellite observations. Lidar-derived cloud heights are used to determine cloud temperatures which are used to estimate cloud emissivities from the satellite IR radiances. These results are then correlated to the observed VIS reflectances for various solar zenith angles

Spin gradient demagnetization cooling of ultracold atoms

A major goal of ultracold atomic physics is quantum simulation of spin Hamiltonians in optical lattices. Progress towards this goal requires the attainment of extremely low temperatures. Here we demonstrate a new cooling method which consists of applying a time-varying magnetic field gradient to a spin mixture of ultracold atoms. We have used this method to prepare isolated spin distributions at positive and negative spin temperatures of +/-50 picokelvin. The spin system can also be used to cool other degrees of freedom, and we have used this coupling to reduce the temperature of an apparently equilibrated sample of rubidium atoms in a Mott insulating state to 350 picokelvin. These are the lowest temperatures ever measured in any system.Comment: 4 pages, 4 figures; (v4) Shortened, added journal re

Student Attainment and the Milwaukee Parental Choice Program

In this report we examine high school completion and postsecondary enrollment (a.k.a. “educational attainment”) of the cohort of 9th grade students who were in the Milwaukee Parental Choice Program (MPCP) at the beginning of our state-mandated evaluation of the MPCP in 2006. After tracking the MPCP 9th graders following the 2006-07 year and comparing them to a carefully matched sample of 9th graders who were in Milwaukee Public Schools (MPS) during the 2006-07 year, we use a combination of parent surveys and administrative (school) records to estimate attainment