Beyond the Spin Model Approximation for Ramsey Spectroscopy

Ramsey spectroscopy has become a powerful technique for probing non-equilibrium dynamics of internal (pseudospin) degrees of freedom of interacting systems. In many theoretical treatments, the key to understanding the dynamics has been to assume the external (motional) degrees of freedom are decoupled from the pseudospin degrees of freedom. Determining the validity of this approximation -- known as the spin model approximation -- is complicated, and has not been addressed in detail. Here we shed light in this direction by calculating Ramsey dynamics exactly for two interacting spin-1/2 particles in a harmonic trap. We focus on $s$-wave-interacting fermions in quasi-one and two-dimensional geometries. We find that in 1D the spin model assumption works well over a wide range of experimentally-relevant conditions, but can fail at time scales longer than those set by the mean interaction energy. Surprisingly, in 2D a modified version of the spin model is exact to first order in the interaction strength. This analysis is important for a correct interpretation of Ramsey spectroscopy and has broad applications ranging from precision measurements to quantum information and to fundamental probes of many-body systems

Three-dimensional color code thresholds via statistical-mechanical mapping

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code on the body-centererd cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D string-like and 2D sheet-like logical operators to be $p^{(1)}_\mathrm{3DCC} \simeq 1.9\%$ and $p^{(2)}_\mathrm{3DCC} \simeq 27.6\%$. We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the 4- and 6-body random coupling Ising models.Comment: 4+7 pages, 6 figures, 1 tabl

A comparison of short-term and long-term air pollution exposure associations with mortality in two cohorts in Scotland

Air pollution–mortality risk estimates are generally larger at longer-term, compared with short-term, exposure time scales. We compared associations between short-term exposure to black smoke (BS) and mortality with long-term exposure–mortality associations in cohort participants and with short-term exposure–mortality associations in the general population from which the cohorts were selected. We assessed short-to-medium–term exposure–mortality associations in the Renfrew–Paisley and Collaborative cohorts (using nested case–control data sets), and compared them with long-term exposure–mortality associations (using a multilevel spatiotemporal exposure model and survival analyses) and short-to-medium–term exposure–mortality associations in the general population (using time-series analyses). For the Renfrew–Paisley cohort (15,331 participants), BS exposure–mortality associations were observed in nested case–control analyses that accounted for spatial variations in pollution exposure and individual-level risk factors. These cohort-based associations were consistently greater than associations estimated in time-series analyses using a single monitoring site to represent general population exposure {e.g., 1.8% [95% confidence interval (CI): 0.1, 3.4%] vs. 0.2% (95% CI: 0.0, 0.4%) increases in mortality associated with 10-μg/m3 increases in 3-day lag BS, respectively}. Exposure–mortality associations were of larger magnitude for longer exposure periods [e.g., 3.4% (95% CI: –0.7, 7.7%) and 0.9% (95% CI: 0.3, 1.5%) increases in all-cause mortality associated with 10-μg/m3 increases in 31-day BS in case–control and time-series analyses, respectively; and 10% (95% CI: 4, 17%) increase in all-cause mortality associated with a 10-μg/m3 increase in geometic mean BS for 1970–1979, in survival analysis]. After adjusting for individual-level exposure and potential confounders, short-term exposure–mortality associations in cohort participants were of greater magnitude than in comparable general population time-series study analyses. However, short-term exposure–mortality associations were substantially lower than equivalent long-term associations, which is consistent with the possibility of larger, more persistent cumulative effects from long-term exposures

Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms

We show that $n$ thermal fermionic alkaline-earth atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the $S_n$ symmetry that permutes atoms occupying different vibrational levels of the trap and the SU($N$) symmetry associated with $N$ nuclear spin states. The high symmetry makes the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU($N$) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary non-thermal distribution.Comment: 12 pages, 5 figures (including supplemental materials

Protected gates for topological quantum field theories

We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators --- for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically-local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons; in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.Comment: 50 pages, many figures, v3: updated to match published versio

The influence of weather-type and long-range transport on airborne particle concentrations in Edinburgh, UK

This study investigated the influence of regional-scale synoptic weather type and geographical source regions of air masses on two-particle concentration metrics (Black Smoke (BS) and PM10) in the city of Edinburgh, UK, between 1981 and 1996. Twenty-seven classifications of Jenkinson Daily Weather Types (JWT) were subdivided into 9 directional categories and 3 vorticity categories, and the influence of JWT category on BS and PM10 determined. Four-day air mass back-trajectories for 1 July 1995–30 June 1996 were computed and grouped into 8 categories depending on the geographical route followed. Significantly elevated concentrations of BS (median values 2, 5 and 4 μg m−3 greater than median for 1981–1996) and PM10 (median values 3, 5.5 and 8 μg m−3 greater than median for 1992–1996) were observed for anticyclonic, southerly and south-easterly weather types, respectively. These differences were not identified at conventional levels of significance for BS in 1995– 1996. This may reflect a shift in more recent times to lower concentrations of predominantly locally emitted BS less affected by regional scale meteorology. Conversely, significant inter-trajectory category differences were observed for PM10 during 1995–1996, with highest concentrations associated with Eastern European trajectories and south-easterly weather type categories (11.4 and 10.7 μg m−3 greater than annual means, respectively). The variation in particle concentration across weather-type was a significant proportion of total median particle concentration, and of a magnitude associated with adverse health outcomes. Thus current PM10 concentrations (and associated health outcomes) in Edinburgh are likely to be significantly influenced by regional-scale meteorology independent of local air quality management areas. Furthermore, changes in long-term trends in distributions of synoptic weather types indicate that future climate change may influence exposure to PM10 and the PM10:BS ratio in Edinburgh. Further definition of the relationships between long-range transport and particle concentration will improve classification of human exposure in epidemiological studies

How brands craft national identity

Drawing on cultural branding research, we examine how brands can craft national identity. We do so with reference to how brands enabled New Zealand’s displaced Pākehā (white) majority to carve out a sense of we-ness against the backdrop of globalization and resurgent indigenous identity claims. Using multiple sources of ethnographic data, we develop a process model of how brands create national identity through we-ness. We find that marketplace actors deployed brands to create and renew perceptions of we-ness through four-stages: reification, lumping, splitting, and horizon expansion. From this, we make three primary contributions to the consumer research literature: we develop a four-part process model of how brands become national identity resources, explore the characteristics of the brands that enable the emergence of and evolution of we-ness, and explore how our processes can address a sense of dispossession among displaced-majorities in similarly defined contexts

Characterization of PM10-bound polycyclic aromatic hydrocarbons and associated carcinogenic risk in Bangkok, Thailand

Concentrations of ambient particulate-bound polycyclic aromatic hydrocarbons (pPAHs) were measured in PM10 samples collected at roadside, industrial and urban background sites in Bangkok between May 2013 and May 2014. The annual average PM10 concentrations were not significantly different between the roadside (56.4 ± 27.3 µg m−3) and industrial (51.0 ± 31.1 µg m−3) sites. The lowest annual mean PM10 was observed at the urban background site (39.8 ± 22.2 µg m−3). Seasonal variations of pPAHs were observed at the three sampling sites. The total pPAHs ranged between 1.09 and 13.10 ng m−3 (mean 4.85 ± 2.51 ng m−3), 1.49 and 9.39 ng m−3 (mean 3.84 ± 2.01 ng m−3) and 0.77 and 5.20 ng m−3 (mean 2.28 ± 1.16 ng m−3) at the roadside, industrial and urban background sites, respectively. The observed annual average benzo[a]pyrene concentrations were 0.47 ± 0.39 ng m−3, 0.35 ± 0.27 ng m−3 and 0.24 ± 0.19 ng m−3 at the roadside, industrial and urban background sites. Long-term carcinogenic health risk of inhalation exposure expressed as the toxicity equivalent to benzo[a]pyrene concentrations were calculated as 0.83, 0.72 and 0.39 ng m−3 at the industrial, roadside and urban background sites, respectively. The composition of pPAHs plays an important role in the carcinogenicity of a PAHs mixture