Net Zero Averted Temperature Increase PDF

W. R. Lindzen, W. Happer and W. A. van Wijngaarden, Atmospheric and Oceanic Physics arXiv: 2406.07392 (2024)

Using feedback-free estimates of the warming by increased atmospheric carbon dioxide (CO2) and observed rates of increase, we estimate that if the United States eliminated net CO2 emissions by the year 2050, this would avert a warming of 0.0084 C, which is below our ability to accurately measure.  If the entire world forced net zero CO2 emissions by the year 2050, a warming of only 0.070 C would be averted.  If one assumes that the warming is a factor of 4 larger because of positive feedbacks, as asserted by the Intergovernmental Panel on Climate Change (IPCC), the warming averted by a net zero US policy would still be very small, 0.034 C.  For worldwide net zero emissions by 2050 and the 4-times larger IPCC climate sensitivity, the averted warming would be 0.28 C.

Effect of Greenhouse Gases on Thermal Emissivity by Clouds PDF

W. A. van Wijngaarden and W. Happer, Atmospheric and Oceanic Physics arXiv: 2401.03061 (2024)

Greenhouse gases, most importantly water vapor, increase the emissivity and decrease the albedo of clouds for thermal radiation.  The modifications, which can be or order 10% for optically thick clouds, depend on the attenuation coefficient of the greenhouse gases, and also on the attenuation coefficient, the single-scattering albedo and the scattering phase function of the cloud particulates.  Cold, high-altitude clouds with low partial pressures of water vapor have smaller emissivities for thermal radiation and larger albedos than otherwise identical but warmer low-altitude clouds with higher partial pressures of water vapor.  In 2n-stream scattering theory, these phenomena can be quantified with the intensity emissivities epsilon_i of the streams i-1, 2, 3,…, 2n, and with upward or downward flux emissivities, epsilon_u and epsilon_d.  The emissivities are the ratios of the outgoing thermal intensities or fluxes to those of a reference black cloud.  Emission from optically-thick, isothermal clouds with scattering as well as absorption and emission, is limb darkened.  Intensity emissivities epsilon_i for streams that are nearly normal to the cloud surface are larger than those of more nearly horizontal streams.  The limb darkening increases with increasing values of the single scattering albedo, omega.  For fixed values of omega, the onset of limb darkening with increasing zenith angle is more abrupt for phase functions with more forward scattering.  Black clouds, which have only absorption and emission but no scattering, have unit (Lambertian) emissivities, epsilon_i-1, for all stream directions.

Radiation Transfer in Cloud Layers PDF

W. A. van Wijngaarden and W. Happer, Atmospheric and Oceanic Physics arXiv: 2310.10622 (2023)

For 2n-stream radiation transfer theory, a stack of m=2, 3, 4,… clouds can be represented as an equivalent loud.  Individual clouds, indexed by c = 1, 2, 3, …, m, are characterized by 2n x 2n scattering matrices S^{c}, that describe how the cloud interacts with 2n streams of axially symmetric incoming radiation, propagating in upward and downward Gauss-Legendre sample directions.  Some of the radiation is transmitted, some is absorbed and converted to heat, and some is scattered into 2n outgoing streams along the directions of the incoming streams.  The clouds are also characterized by 2n x 1 thermal source vectors |J^{c}} that describe the thermal emission of radiation along the stream directions by cloud particulates and gas molecules.  The 2n x 2n scattering matrix for the equivalent cloud, S^{ev} = S^{m} * S^{m-1}* … * S^{2}*S^{1}, is the Redheffer star product of the scattering matrices S^{c} of the individual clouds.  The 2n x 1 thermal source vector for the equivalent cloud, |J^{ev}} = G^{m,m} |J^{m}} + G^{m,m-1}|J^{m-1} + …  + G^{m,2}\J^{2}} + G^{m,1}|J^{1}}, is a linear combination of the thermal source vectors |J^{c}} of the individual clouds.  The 2n x 2n discrete Green’s matrices G^{m,c} can be constructed from the scattering matrices S^{c} of individual clouds.  The equivalent scattering matrix S^{ev} and the equivalent thermal source vector |J^{ev}} are analogous to the equivalent resistance and the equivalent electromotive force (emf) of Thevenin’s theorem for a network of electrical circuits.  Illustrative numerical examples re given for single clouds, 3-cloud stacks and 10-cloud stacks.  These methods are useful for modeling radiation transfer in Earth’s atmosphere, which can be represented by layers of invisible clouds, consisting of clear air and greenhouse gases, or visible clouds which also include condensed water, smog, etc.

Instantaneous Clear Sky Radiative Forcings of Halogenated Gases PDF

W. A. van Wijngaarden and W. Happer, Atmospheric and Oceanic Physics arXiv: 2306.13642 (2023)

The clear sky instantaneous radiative forcings of the 14 halogenated gases previously shown to have the largest contribution to global warming, were found. The calculation used the absorption cross sections for the halogenated gases which are assumed to be independent of temperature as well as over 1/3 million line strengths for the five main naturally occurring greenhouse gases: H2O, CO2, O3, CH4 and N2O, from the Hitran database. The total radiative forcing of the halogenated gases at their 2020 concentrations is 0.52 (0.67) W/m² at the tropopause (mesopause). Over half of this forcing is due to CFC11 and CFC12 whose concentrations are steadily declining as a result of the Montreal Protocol. The rate of total forcing change for all 14 halogenated gases is 1.5 (2.2) mW/m²/year at the tropopause (mesopause). The calculations assumed a constant altitude concentration for all halogenated gases except CFC11, CFC12 and SF6. Using the observed altitude dependence for those 3 molecules reduced their radiative forcings by about 10%. The global warming potential (GWP) values were found to be comparable to those given by the Intergovernmental Panel on Climate Change. The contribution of a gas to global warming can be estimated using the forcing power per molecule defined as the derivative of its radiative forcing with respect to its column density. For the present atmosphere, the per-molecule forcing powers of halogenated gases are orders of magnitude larger than those for the 5 naturally occurring greenhouse gases because the latter have much higher concentrations and are strongly saturated. However, the rates of concentration increase of the 5 main greenhouse gases are orders of magnitude greater than that of any halogenated gas. Assuming the temperature increase caused by each gas is proportional to its radiative forcing increase, the 14 halogenated gases are responsible for only 2% of the total global warming.

Impact of Changing Greenhouse Gas Concentrations on Ontario’s Climate PDF

W. A. van Wijngaarden, Atmospheric and Oceanic Physics arXiv: 2305.05500 (2023)

The effect of changing greenhouse gas concentrations, most notably carbon dioxide, CO2, on climate was examined.  In particular, calculations of the climate sensitivity, the warming of the Earth due to a doubling of atmospheric carbon dioxide, are discussed.  Greenhouse gas concentrations, as determined from air bubbles trapped in ice as well as at Mauna Loa, Hawaii are presented.  The greenhouse gas amounts generated by Canada and Ontario were used to estimate their respective contributions to global warming.  Ontario was responsible for only 035% of the world’s CO2 emissions in 2019 and this amount was 20% lower than in 2005.  The predictions of Global Climate Models (GCMs) regarding temperature, polar ice caps, oceans, precipitation and extreme events were compared to observations.  Records since 1880 show an overall warming of about 1 ^oC  However, the GCMs do not account for observed decadal temperature fluctuations and consistently overestimate the warming.  Ontario’s contribution to global warming is only 9.2 x 10^{-5  o}C/year using the Intergovernmental Panel on Climate Change (IPCC) recommended climate sensitivity value.  Measurements of the polar ice caps reveal a decrease in the minimum September Arctic sea ice extent during 1979-2022 but the trend levelled off after 2007; while the average Antarctic sea ice extent slightly increased.  Sea level increased slightly throughout the 20th century.  Ontario’s contribution to anthropogenic sea level rise is about 0.005 mm/year.  Sea level along Ontario’s Hudson Bay coast is decreasing due to isostatic rebound of the land following the last Ice Age.  The change to ocean acidity due to CO2 absorption from the atmosphere is negligible compared to that due to tides, ocean depth and seasonal effects.  Ontario’s contribution to ocean acidification is estimated to be 6 x 10^-6 pH /year.  No changes in precipitation in North America over the 19th and 20th centuries, nor at Toronto since 1843, were found.  The Great Lake levels are remarkably constant over the past century showing no evidence of a change in the incidence of flooding.  No evidence was found that the frequency of extreme events such as hurricanes or tornadoes increased during recent decades.  The number of forest fires in Canada and Ontario decreased during 1990 to 2020.

Atmosphere and Greenhouse Gas Primer PDF

W. A. van Wijngaarden &  W. Happer, Atmospheric and Oceanic Physics arXiv: 2303.00808  (2023)

We discuss the basic ways greenhouse gases affect radiation transfer in Earth’s atmosphere.  We explain how greenhouse gases like water vapor or carbon dioxide differ from non-greenhouse gases like nitrogen or oxygen.  Using simple thermodynamics and fluid mechanics, we show that the atmosphere of a planet with sufficiently high concentrations of greenhouse gases must develop a convecting troposphere between the surface and the tropopause altitude.  The planet must also develop a non-convecting stratosphere for altitudes above the tropopause.  In the simplest approximation of an atmosphere that is transparent to sunlight and has frequency-independent opacity for thermal radiation (an infrared gray troposphere), one can find simple formulas for the tropopause altitude, and for the latitude profiles of pressure and temperature.  The troposphere is nearly isentropic and the stratosphere is nearly isothermal.  The real atmosphere of the Earth is much more complicated than the simple model, but it does have a troposphere and a stratosphere.  Between the surface and the tropopause the entropy per kilogram of real tropospheric air increases slowly with altitude.  The entropy increases much more rapidly with altitude in the stratosphere.  The stratosphere has a nearly isothermal lower part and a hotter upper part due to absorption of solar ultraviolet radiation by ozone.  The thermal opacity of the real atmosphere has a complicated frequency dependence due to the hundreds of thousands of vibration-rotation transitions of its greenhouse molecules.  Unlike the simple model where nearly all radiation to space originates at the tropopause altitude, radiation to space from Earth’s real atmosphere originates from both the surface and all altitudes in the troposphere.  A small additional amount of radiation originates in the stratosphere.  When these complications are taken into account, model calculations of the thermal radiation spectrum at the top of the atmosphere can hardly be distinguished from those observed from satellites.

2n-Stream Thermal Emission from Clouds PDF

W. A. van Wijngaarden &  W. Happer, Atmospheric and Oceanic Physics arXiv:  (2023)

We analyze thermal emission of radiation in homogeneous clouds.  The clouds have negligible horizontal variation, but the temperature can vary in the vertical direction. The radiation at the optical depth τ above the bottom of the cloud is characterized by the intensity values I(μ_i,τ)  at 2n Gauss-Legendre direction cosines μ_i, the roots of the 2n-th Legendre polynomial, P_2n(μ_i)=0.  Scattering matrices are used to describe the fraction of intensity with incoming direction cosine μ_i’ that is scattered to intensity with outgoing direction cosine μ_i.  Green’s-function matrices are used to describe radiation generated by  infinitesimally thin layers of cloud particulates, thermally emitting at the source optical depth τ’.  For thin isothermal clouds of optical thickness τ_c ≤ 1, thermal emission is mainly determined by the single scattering albedo ϖ. The emitted intensity of thin clouds is limb brightened and depends little on the  scattering phase function.  For optically thick isothermal clouds, with τ_c  >> 1, purely absorbing clouds with ϖ = 0 become perfect blackbodies and emit isotropic Planck intensity, and have neither limb brightening nor darkening. Thick isothermal  clouds with moderate single scattering albedos emit substantially less thermal radiation than black bodies, and the emission depends strongly on the anisotropy of the scattering phase function.  Clouds with strong forward scattering  are “blackest” and emit the most thermal radiation. There is limb darkening, which is most pronounced for strongly forward-scattering phase functions. The limb darkening in thick, isothermal, scattering clouds is not due to temperature gradients, as it is for the Sun.  With scattering, nearly vertical radiation produced by thermal emission escapes through the surface more efficiently than nearly horizontal radiation. For isothermal clouds, the scattered and emitted intensities obey Kirchhoff’s laws of thermal radiation. For clouds with hot interiors, there is limb darkening even for purely absorbing particulates. Radiative conduction of heat inside optically thick clouds is orders of magnitude faster than conduction due to molecular diffusion.

Nitrous Oxide and Climate PDF

C. A. de Lange, J. D. Ferguson, W. A. van Wijngaarden &  W. Happer CO2 Coalition (2022)

Higher concentrations of atmospheric nitrous oxide (N2O) are expected to slightly warm Earth’s surface because of increases in radiative forcing.  Radiative forcing is the difference in the net upward thermal radiation flux from the Earth through a transparent atmosphere and radiation through an otherwise identical atmosphere with greenhouse gases.  Radiative forcing, normally measured in W m^-2, depends on latitude, longitude and latitude, but it is often quoted for the tropopause, about 11 km of altitude of temperature latitudes, or for the top of the atmosphere at around 90 km.  For current concentrations of greenhouse gases, the radiative forcing per added N2O molecule, is about 230 times larger than the forcing per added carbon dioxide (CO2) molecule.  This is due to the heavy saturation of the absorption band of the relatively abundant greenhouse gas, CO2, compared to the much smaller saturation of the absorption bands of the trace greenhouse gas N2O.  But the rate of increase of CO2 molecules, about 2.5 ppm/year (ppm = part per million by mole), is about 3000 times larger than the rate of increase of N2O molecules, which has held steady at around 0.00085 ppm/year since 1985.  So the contribution of nitrous oxide to the annual increase in forcing is 230/3000 or about 1/13 that of CO2  If the main greenhouse gases, CO2, CH4 and N2O have contributed about 0.1 C/decade of the warming observed over the past few decades, this would correspond to about 0.00064 K per year or 0.064 K per century of warming from N2O.  Proposals to place harsh restrictions on nitrous oxide emissions because of warming fears are not justified by these facts.  Restrictions would cause serious harm, for example by jeopardizing world food supplies.

2n-Stream Conservative Scattering PDF

W. A. van Wijngaarden &  W. Happer Atmospheric and Oceanic Physics arXiv:  2207.03978 (2022)

We show how to use matrix methods of quantum mechanics to efficiently and accurately calculate axially symmetric radiation transfer in clouds, with conservative scattering of arbitrary anisotropy.   Analyses of conservative scattering, where the single scattering albedo is  ϖ = 1 and no energy is exchanged between the radiation and scatterers, began with work by Schwarzschild, Milne, Eddington and others on radiative transfer in stars.  There, the scattering is isotropic or nearly so.  It has been difficult to extend traditional methods to highly anisotropic scattering, like that of sunlight in Earth’s clouds.  The 2n-stream method described here is a practical way to handle highly anisotropic, conservative scattering.  The basic ideas of the 2n-stream method are an extension of Wick’s seminal work on transport of thermal neutrons by isotropic scattering to scattering with arbitrary anisotropy.  How to do this for finite absorption and ϖ < 1 was described in a previous paper.  But those methods fail for conservative scattering, when ϖ =1.  Here we show that minor modifications to the fundamental 2n-scattering theory for ϖ < 1 make it suitable for ϖ =1.

2n-Stream Radiative Transfer PDF

W. A. van Wijngaarden &  W. Happer Atmospheric and Oceanic Physics arXiv:  2205.09713 (2022)

We use 2n = 2, 4, 6, … “streams” of axially symmetric radiation to solve the equation of transfer for a layered medium.  This is a generalization of Schuster’s classic 2-stream model.  As is well known, using only the first 2n Legendre polynomials to describe the angular dependence of radiation reduces the equation of transfer to a first order differential equation in a space of 2n dimensions.  It is convenient to characterize the radiation as 2n stream intensities I(μ_i), propagating at angles close to the zenith angles θ_i = cos^-1 = μ_i.  The 2n Gauss-Legendre cosines i are defined by P_2n(μ_i) = 0, where P_2n(μ) is the Legendre polynomial of degree 2n.  We show how to efficiently and accurately solve the equation of transfer with vector and matrix methods analogous to those used to solve Schrodinger’s equation of quantum mechanics.  To model strong forward scattering, like that of visible light by Earth’s clouds, we have introduced a new family of phase functions ϖ^{p}(μ).  These give the maximum possible forward scattering ϖ^{p}(μ=1) = p(p+1), for a phase function constructed from the first 2p = 2, 4, 6, … Legendre polynomials.  We show illustrative examples of radiative-transfer phenomena calculated with this new method.

Relative Potency of Greenhouse Molecules PDF

W. A. van Wijngaarden &  W. Happer Atmospheric and Oceanic Physics arXiv:  2006.03098 (2021)

The forcings due to changing concentrations of Earth’s five most important, naturally occurring greenhouse gases, H2O, CO2, O3, N2O and CH4 as well as CF4 and SF6 were evaluated for the case of a cloud-free atmosphere.  The calculation used over 1.5 million lines having strengths as low as 10^-27 cm.  For a hypothetical, optically thin atmosphere, where there is negligible saturation of the absorption bands, or interference of one type of greenhouse gas with others, the per-molecule forcings are of order 10^-22 W for H2O, CO2, O3, N2O and CH4, and of order 10^-21 W for CF4 and SF6.  For current atmospheric concentrations, the per-molecule forcings of the abundant greenhouse gases H2O and CO2 are suppressed by four orders of magnitude.  The forcings of the less abundant greenhouse gases, O3, N2O and CH4, are also suppressed, but much less so.  For CF4 and SF6, the suppression is less than an order of magnitude because the concentrations of these gases is very low.  For current concentrations, the per-molecule forcings are two to four orders of magnitude greater for O3, N2O, CH4, CF4 and SF6 than those of H2O and CO2.  Doubling the current concentrations of CO2, N2O or CH4 increases the forcings by a few percent.  A concentration increase of either CF4 or SF6 by a factor of 100 yields a forcing nearly an order of magnitude smaller than that obtained by doubling CO2.  Important insight was obtained using a harmonic oscillator model to estimate the power radiated per molecule.  Unlike the most intense bands of the 5 naturally occurring greenhouse gases, the frequency-integrated cross sections of CF4 and SF6 were found to noticeably depend on temperature.

Dependence of Earth’s Thermal Radiation on Five Most Abundant Greenhouse Gases PDF

W. A. van Wijngaarden &  W. Happer Atmospheric and Oceanic Physics arXiv:  2006.03098 (2020)

The atmospheric temperatures and concentrations of Earth’s five most important greenhouse gases, H2O, CO2, O3, N2O and CH4 control the cloud-free, thermal radiative flux from the Earth to outer space.  Over 1/3 million lines having strengths as low as 10^-27 cm of the HITRAN database were used to evaluate the dependence of the forcing on the gas concentrations.  For a hypothetical, optically thin atmosphere, where there is negligible saturation of the absorption bands, or interference of one type of greenhouse gas with others, the per-molecule forcings are of order 10^-22 W for H2O, CO2, O3, N2O and CH4.  For current atmospheric concentrations, the per-molecule forcings of the abundant greenhouse gases H2O and CO2 are suppressed by four orders of magnitude.  The forcings of the less abundant greenhouse gases, O3, N2O and CH4, are also suppressed, but much less so.  For current concentrations, the per-molecule forcings are two to three orders of magnitude greater for O3, N2O and CH4, than those of H2O or CO2.  Doubling the current concentrations of CO2, N2O or CH4 increases the forcings by a few per cent.  These forcing results are close to previously published values even though the calculations did not utilize either a CO2 or H2O continuum.  The change in surface temperature due to CO2 doubling is estimated taking into account radiative-convective equilibrium of the atmosphere as well as water feedback for the cases of fixed absolute and relative humidities as well as the effect of using a pseudoadiabatic lapse rate to model the troposphere temperature.  Satellite spectral measurements at various latitudes are in excellent quantitative agreement with modelled intensities.

Methane and Climate PDF

W. A. van Wijngaarden &  W. Happer (2019)

Atmospheric methane (CH4) contributes to the radiative forcing of Earth’s atmosphere.  Radiative forcing is the difference in the net upwards thermal radiation from the Earth through a transparent atmosphere and radiation through an otherwise identical atmosphere with greenhouse gases.  Radiative forcing, normally specified in units of W m^-2, depends on latitude, longitude and altitude, but it is often quoted for a representative temperature latitude, and for the altitude of the tropopause or for the top of the atmosphere.  For current concentrations of greenhouse gases, the radiative forcing at the tropopause, per added CH4 molecule, is about 30 times larger than the forcing per added carbon dioxide (CO2) molecule.  This is due to the heavy saturation of the absorption band of the abundant greenhouse gas, CO2.  But he rate of the increase of CO2 molecules, about 2.3 ppm/year (ppm = part per million), is about 300 times larger than the rate of increase of CH4 molecules, which has been around 0.0076 ppm/year since 2008.  So the contribution of methane to the annual increase in forcing is one tenth (30/300) that of carbon dioxide.  The net forcing increase from CH4 and CO2 increases is about 0.05 W m^-2 year^-1.  other things being equal, this will cause a temperature increase of about 0.012 C year^-1.  Proposals to place harsh restrictions on methane emissions because of warming fears are not justified by facts.

Seasonal and Annual Trends in Australian Minimum/Maximum Daily Temperatures PDF

W. A. van Wijngaarden & A. Mouraviev, accepted Open Atmospheric Journal (2016)

Seasonal and annual trends in Australian minimum and maximum temperature were studied.  Records of daily minimum and maximum temperatures averaged over each month, extending as far back as 1856 were examined.  Over 1/2 million monthly temperature values were retrieved from the Australian Bureau of Meteorology for 299 stations.  Each station had an average of 89 years of observations.  Significant step discontinuities affected the maximum temperature data in the 19^th century when Stevenson screens were installed.  The temperature trends were found after such spurious data were removed and averaged over all stations.  The resulting trend in the minimum (maximum) daily temperature was 0.67 ± 0.19 (0.58 ± 0.26) ^oC per century for the period 1907-2014.  Decadal fluctuations were evident in the maximum daily temperature with most of the increase occurring in the late 20^th century.  The minimum and maximum daily temperature trends were also found for the various seasons.  The minimum daily temperature trend exceeded the maximum daily temperature trend for all seasons except during June to August.  The largest increase in minimum temperature as well as the smallest maximum temperature increases were found for the region north of 30 ^oS latitude and east of 140 ^oE longitude.  There was also evidence that urban stations had greater increases in maximum daily temperature than those located in a rural environment.

Is Global Warming Hot Air? PDF

W. A. van Wijngaarden, 153 pages (2016)

There have been increasing shrill warnings over the past 20 years about mankind’s effect on the climate.  These primarily arise due to the combustion of fossil fuels that releases carbon dioxide into the atmosphere.  The most recent report of the Intergovernmental Panel on Climate Change states “Warming of the climate system is unequivocal”.  it has led to record melting of the Arctic ice cap, rising sea levels, ocean acidification as well as changes in precipitation and more severe storms.  The preponderance of scientists apparently support this view and strongly encourage drastic action be undertaken to decrease our use of fossil fuels.  Indeed, President Obama has stated “climate change is settled science”.  However, some scientist express varying levels of concern about some of these climate change claims.  This book presents and discusses some of the evidence.

Manipulation of Ultracold Atoms using Double-Loop Microtraps PDF

W. A. van Wijngaarden, B. Jian & A. Mouraviev, Physica Scripta 91, 054001 (2016)

Ultracold atoms created using microtraps are being used in an increasing number of diverse applications.  This paper reviews the double-loop microtrap which consists of two concentric circular wire loops carrying oppositely oriented currents.  This generates a magnetic field configuration that traps a magnetic dipole in three dimensions.  The position of the trapped atoms relative to the atom chip surface containing the microwire loops, can be precisely controlled by applying different currents in the two loops or alternatively using a so called bias magnetic field oriented perpendicular to the chip surface.  Double-loop microtraps can be daisy chained in series to create a one or two dimensional microtrap array.  Experiments that have demonstrated a double-loop microtrap array are discussed.  Future possibilities are presented as to how atoms can be transferred between adjacent microtraps as well as the use of an additional micro sized Ioffe coil to create a trap having a nonzero magnetic field minimum to reduce atom loss by suppressing Majorana transitions.

Changes in Annual Precipitation over the Earth’s Land Mass excluding Antarctica from the 18th century to 2013 PDF

W. A. van Wijngaarden & A. Syed, Journal of Hydrology 531, 1020 (2015)

Precipitation measurements made at nearly 1,000 stations located in 114 countries were studied.  Each station had at least 100 years of observations resulting in a dataset comprising over 1.5 million monthly precipitation amounts.  Data for some stations extend back to the 1700s although most of the data exist for the period after 1850.  The total annual precipitation was found if all monthly data in a given year were present.  The percentage annual precipitation change relative to 1961-90 was plotted for 6 continents; as well as for stations at different latitudes and those experiencing low, moderate and high annual precipitation totals.  The trends for precipitation change together with their 95% confidence intervals were found for various periods of time.  Most trends exhibited no clear precipitation change.  The global changes in precipitation over the Earth’s land mass excluding Antarctica relative to 1961-90 were estimated to be:  -1.2 +/- 1.7, 2.6 +/- 2.5 and -5.4 +/- 8.1 % per century for the periods 1850-2000, 1900-2000 and 1950-2000, respectively.  A change of 1% per century corresponds to a precipitation change of 0.09 mm/year.

Arctic Temperature Trends from the early 19th Century to the present PDF

W. A. van Wijngaarden, Theoretical & Applied Climatology 122, 567 (2015)

Temperatures were examined at 118 stations located in the Arctic and compared to observations at 50 European stations whose records averaged 200 years and in a few cases extend to the early 1700s.  Nearly all stations exhibited warming trends.  For each station, the temperature relative to the average value during 1961-1990 was found.  The resulting temperature change averaged over the Arctic stations was plotted.  For the period 1820-2014, trends were found for the January, July and annual temperatures of 1.0, 0.0 and 0.7 oC per century, respectively. Decadal variations are evident and much of the temperature increase occurred during the 1990s. Over the past century, Siberia, Alaska and Western Canada have experienced somewhat greater warming than Eastern Canada, Greenland and Northern Europe.  The temperature change experienced by the Arctic stations during the last two centuries closely tracks that found for the European stations.

A Linear Array of 11 Double-Loop Microtraps for Ultracold Atoms PDF

B. Jian & W. A. van Wijngaarden, J. Phys. B 47, 215301 (2014)

A linear array of 11 closely spaced microtraps was demonstrated. Each microtrap was created using the magnetic field generated by two concentric circular wire loop  having radii of 60 and 132 μm carrying oppositely oriented currents as well as a bias magnetic field oriented perpendicular to the atom chip surface containing the microwire loops.  ⁸⁷Rb atoms were initially cooled using either a surface magneto-optical trap (MOT) or a far off resonance optical dipole trap (FORT) created using an infrared laser directed along the microtrap array axis.  The microtrap current was turned on and over 12,000 atoms were loaded into each microtrap.  The advantage of FORT loading was that the 11 microtraps were about equally populated and the microtrapped atom temperature of 11 μK was one quarter of that obtained using the MOT.

Temperature Trends in the Canadian Arctic during 1895-2014 PDF

W. A. van Wijngaarden, Theoretical & Applied Climatology 120, 609 (2015)

The average January, July and annual temperatures were examined at 27 stations located in the Canadian Arctic.  Some of these station have temperature records extending as far back as 1895.  Nearly all stations exhibited warming trends.  For each station the difference between the temperature relative to the average value found during 1961-1990 was found.  The resulting temperature change averaged over the 27 stations was then plotted to give a time series covering the period 1895-2014.  Trends were found for the January, July and annual temperatures of 3.1, 1.6 and 1.9 oC per century, respectively.  Similar trends were found in the western and eastern Arctic.  The warming occurred primarily in the first and last decades of the 20th century.  For the period 1915-1995 the annual temperature trend was only 0.4 oC per century.

Examination of Archival Data for Inhomogeneities and Determination of Climate Change in North America PDF

W. A. van Wijngaarden, Journal of Earth Science and Engineering 3, 776 (2014)

Numerous articles have examined archival weather observations and attributed climate changes on time scales ranging from centuries to decades and in one case even days to human activity.  This article gives examples showing how climate variability and sudden changes in instruments affect trend determination.  In particular, surface temperature and water vapor pressure trends in North America during 1948-2010 are discussed.  Over ¼ billion hourly observations taken at 309 stations, were first carefully examined for inhomogeneities.  Positive and negative steps, for both temperature and water vapor pressure were found to not be evenly distributed in time.  Inclusion of such data in a trend analysis would overstate decadal changes in temperature and water vapor. Time series free of such discontinuities show a statistically significant warming has primarily affected the western Arctic, Canadian prairies and the Midwestern U.S. during winter.  Increases in water vapor pressure are most pronounced in summer in the eastern U.S.  The decadal water vapor pressure trends are somewhat smaller than found in other studies that examined data for far shorter time periods.  The claim of a change in the diurnal temperature range (DTR) during the 3 day flight ban following Sept. 11, 2011, is not substantiated.  The observed change in the DTR was likely caused by a reduction in cloudiness during the flight ban.

Comparison of Loading Double-loop Microtraps from a Surface MOT and a FORT PDF

B. Jian & W. A. van Wijngaarden, Appl. Physics B:Lasers & Optics. DOI 10.1007/s00340-013-5573-4 (2013)

Two methods to load a microtrap consisting of two concentric microwire loops of radii 300 and 660 microns carrying oppositely oriented currents, are demonstrated. Atoms can be directly loaded into the microtrap from a surface magneto-optical trap (MOT) or alternatively using a far-off resonance optical dipole trap (FORT) as an intermediate step. About 1 x 10^{5 87}Rb atoms can be loaded into the microtrap using either technique although the FORT achieves a lower temperature. The Fort is well suited to loading a linear array of 3 microtraps that are aligned with the propagation direction of the infrared laser. Atoms can be trapped in either the 5S_1/2 F=1 or 2 ground state hyperfine level. The position of the microtrapped atom cloud can be precisely adjusted using a bias magnetic field over a distance of 350 to slightly less than 50 microns from the atom chip surface.

A Double-Loop Microtrap for Ultracold Atoms PDF

B. Jian & W. A. van Wijngaarden, Journal Optical Society of America B, 30, No. 2, 238-243 (2013)

A microtrap consisting of two concentric circular wire loops having radii of 300 and 660 microns respectively, is demonstrated. The 3 dimensional trap has a maximum depth of over 1 milliKelvin and the trap center position as measured below the atom chip surface can be adjusted by applying a small bias magnetic field. Over 10^{5 87}Rb atoms were transferred into the microtrap from a magnetooptical trap and remained trapped for several hundred milliseconds which is limited by the background pressure. The loading of a linear array of 3 microtraps is also demonstrated. The trap dimensions are readily scaled to micron size which is of interest for creating a one and two dimensional array of neutral atom traps on a single atom chip.

Advances in Laser Spectroscopy of Lithium PDF

W. A. van Wijngaarden & B. Jian, European Physical Journal D, 222, 2057-2066 (2013)

A number of recent experiments have employed novel spectroscopic techniques to precisely measure the fine and hyperfine structure splittings as well as the isotope shifts for several transitions at optical frequencies for the stable ^6,7Li and radioactive isotopes ^8,9,11Li. These data offer an important test of theoretical techniques that have been developed over the last decade by two groups to accurately calculate effects due to Quantum Electrodynamics and the finite nuclear size in 2 and 3 electron atoms. Theory and experiment have studied several transitions in both singly ionized and neutral lithium. The work by multiple groups permits a critical examination of the consistency of separately, the experimental work as well as the theoretical calculations. Combining the measured isotope shifts with the calculated energy shifts passing these consistency tests, permits the determination of the relative nuclear charge radius with an uncertainty approaching 1 x 10^-18 meter. These results are more than an order of magnitude more accurate than those obtained by electron scattering experiments and give insight into the mass and charge distributions of the nuclear constituents. Prospects for a precision measurement of the fine structure constant are also discussed.

Examination of Diurnal Temperature Range at stations in Continental U.S. during Sept. 8-17, 2001 PDF

W. A. van Wijngaarden, Theoretical & Applied Climatology, 109, Issue 1, 1-5, (2012)

The tragic events of Sept. 11, 2001 resulted in suspension of commercial flights over North America. It has been suggested the diurnal temperature range (DTR) increased due to an absence of airplane contrails. This study examined hourly data observed at 288 stations. The average DTR, temperature, maximum/minimum temperature and relative humidity were found for each day in 2001 and compared to the average value occurring during 1975-2005. For the coterminous U.S., the DTR averaged over the period Sept. 11-14, 2001 was about 1 ^oC larger than that found for the 3 days prior and after the flight ban. However, the day to day DTR does not correlate well with the flight ban. Plots of the change in DTR throughout North America during Sept. 8-17 show changes consistent with the natural progression of weather systems.

Surface Water Vapor Pressure and Temperature Trends in North America during 1948-2010 PDF

V. Isaac & W. A. van Wijngaarden, J. Climate 25, No. 10, 3599-3609 (2012)

Over ¼ billion hourly values of temperature and relative humidity observed at 309 stations located across North America during 1948-2010 were studied. The water vapor pressure was determined and seasonal averages were computed. Data were first examined for inhomogeneities using a statistical test to determine whether the data was fit better to a straight line or a straight line plus an abrupt step which may arise from changes in instruments and/or procedure. Trends were then found for data not having discontinuities. Statistically significant warming trends affecting the Midwestern U.S., Canadian prairies and the western Arctic are evident in winter and to a lesser extent in spring while statistically significant increases in water vapor pressure occur primarily in summer for some stations in the eastern half of the U.S. The temperature (water vapor pressure) trends averaged over all stations were 0.30 (0.07), 0.24 (0.06), 0.13 (0.11), 0.11 (0.07) ^oC/decade (hPa/decade) in the winter, spring, summer and autumn seasons, respectively. The averages of these seasonal trends are 0.20 ^oC/decade and 0.07 hPa/decade which correspond to a specific humidity increase of 0.04 g/kg per decade and a relative humidity reduction of 0.5%/decade.

Critical Examination of Isotope Shift & Fine Structure Measurements for ^6,7Li Transitions PDF

G. A. Noble & W. A. van Wijngaarden, Canadian Journal of Physics, 87, 807-815 (2009)

Precise isotope shift and fine structure measurements are critically reviewed. Each experiment was checked whether data found for different transitions yielded consistent values for the relative nuclear charge radius squared ∆r² of ^6,7Li. Experiments that passed this test found ∆r² = 0.735 ± 0.036, 0.755 ± 0.023 and 0.739 ± 0.013 fm² by studying the Li⁺ 1s2s ³S₁ 1s2p ³P transition, the Li D lines and the Li 2S_1/2 – 3S_1/2 transition, respectively. These data determine the relative nuclear charge radius 25 times more accurately than electron scattering. Similarly, averaging the most reliable fine structure data gives 62,678.75 ± 0.55 MHz for the ⁷Li⁺ 1s2p ³P_1,2 interval in good agreement with theory. The results for the ^6,7Li 2P fine structure intervals, 10,052.954 ± 0.049 and 10,053.154 ± 0.040 MHz, exceed computed values by 2 MHz and yield a specific isotope shift which is nearly a factor of 2 lower than a theoretical estimate.

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Precision Laser Spectroscopy of Li⁺ and Neutral Lithium PDF

W. A. van Wijngaarden & G. Noble, Springer Verlag Lecture Notes in Physics, 745, 111-129 (2008)

Lithium has a number of properties that make it useful for both experimental and theoretical study. Precise spectroscopic measurements of optical transitions in both Li⁺ and neutral Li are reviewed. Experiments have yielded hyperfine and fine structure splitting that test QED as well as isotope shifts that determine the relative nuclear charge radius between isotopes to an accuracy of 2 x 10^-17 m. Experimental and theoretical results agree very well for Li⁺ and a measurement of the fine structure of the 1s2p ³P_0,1,2 levels is of interest to determine the fine structure constant. For neutral lithium, additional theoretical work is needed to match the experimental accuracy of the 2P fine structure splitting.

Study of the Rb D2 Transition Linewidth at Ultralow Temperatures PDF

B. Schultz, H. Ming, G. Noble & W. A. van Wijngaarden, European Physical Journal D 48, 171-176, (2008)

The Rb D2 linewidth was studied using atoms cooled to a temperature of 50 μK that were contained in a magneto-optical trap. The transmission of a probe laser through the atom cloud was monitored using a CCD detector. The frequency of the probe laser was scanned across the resonance using an acousto-optic modulator. The observed lineshape was very well fitted by a Lorentzian function. The full width half maximum linewidth was examined as a function of the optical depth and the probe laser intensity. The extrapolated value at zero optical depth 6.062 ± 0.017 MHz corresponds to a 5P_3/2 lifetime of 26.25 ± 0.07 nsec. This result agrees with lifetimes found in experiments that measured the temporal decay of fluorescence or photoassociation spectroscopy and is somewhat below the result of a relativistic many body perturbation calculation.

Climate Change During 1953-2007 in the Canadian Arctic PDF

W. A. van Wijngaarden, The Pacific & Arctic Oceans: New Oceanographic Research, Nova Science, (2008)

Hourly measurements of relative humidity, temperature and pressure along with daily precipitation totals recorded at 26 stations in the Canadian Arctic during 1953-2007 were analyzed. The data were first checked for discontinuities. A sudden decrease in relative humidity occurred in the 1970s and 1980s due to an instrument change making it impossible to reliably discern a relative humidity trend due to climate change. A statistically significant warming averaging 5.6 ˚C has occurred in winter over the Western Arctic but no change was found in either the Eastern or Northern Arctic. Precipitation varied considerably from year to year and no trends were evident. A statistically significant pressure change averaging -5.8 hPa occurred during winter. The observed temperature increase and pressure decrease during winter may be indicative of changing circulation patterns.

Transfer of Ultracold ⁸⁷Rb from a QUIC Magnetic Trap into a Far Off Resonance Optical Trap PDF

H. Ming & W. A. van Wijngaarden, Canadian Journal of Physics, 85, 247-358 (2007)

Ultracold ⁸⁷Rb atoms were transferred from a QUIC magnetic trap into a far off resonance optical trap (FORT). FORTs were created by focusing a 150 mW laser beam having a wavelength of 852 nm to a spot having a radius of 20 and 30 um. A probe laser then passed through the ultracold atom cloud after the magnetic trap was turned off to study the temporal evolution of the optically trapped atoms. Nearly a million atoms could be transferred into the FORT at temperatures as low as 1 microKelvin with an efficiency as high as 50%.

Surface Temperature and Humidity Trends in Canada for 1953-2005 PDF

L. Vincent, W. A. van Wijngaarden & R. Hopkinson, Journal of Climate, 20, 5100-5113 (2007)

Annual and seasonal trends in temperature, dew point, relative humidity and specific humidity are presented for the period 1953-2005. The analysis uses hourly observations from 75 climatological stations across Canada. Data were examined for discontinuities due to change sin instruments and observing practice. It was found that the main discontinuity corresponds to the replacement of the psychrometer by the dewcel in the early 1970s which created an artificial negative step in relative humidity and dew point at many locations. After accounting for these discontinuities, the result of trend analysis show evidence of increase in air moisture content associated with the warming observed in the country. During winter and spring, the significant warming in the western and southern regions is accompanied by an increase in dew point and specific humidity and by a decrease in relative humidity in summer, warming is observed in the southeast and it is associated with significant positive trends in dew point and specific humidity. Although there is no strong evidence of a greater nighttime warming in Canada over 1953-2005, the nighttime dew point and specific humidity trends are slightly larger and the daytime trends, especially during the spring and summer.

Isotope Shifts & Fine Structures of ^6,7Li D Lines & Determination of Relative Nuclear Charge Radius PDF

G. Noble, B. Schultz, H. Ming & W. A. van Wijngaarden, Physical Review A, 74, 012502 (2006)

The ^6,7Li D lines were excited using an electro-optically modulated CW dye laser that intersected an atomic beam. Fluorescence was recorded as the laser was scanned across the resonance. Hence, each transition was multiply excited allowing for calibration of the frequency scan. The ^6,7Li 2P fine structures were found to be 10052.964 ± 0.050 and 10053.119 ± 0.058 MHz. The D1 and D2 isotope shifts were determined to be 10534.039 ± 0.070 and 10534.194 ± 0.104 MHz, which imply values for the ^6,7Li relative nuclear charge radius that agree to 20 millifermi.

Bose Einstein Condensation & Quantum Information: A Second Century of Einstein? PDF

W. A. van Wijngaarden, Canadian Journal of Physics, 83, 671-685 (2005)

A century ago Albert Einstein transformed classical physics with his seminal papers on Brownian motion, the Photoelectric effect and of course special and later general relativity. Lesser well known are his contributions to Bose Einstein Condensation and the Einstein Podolsky Rosen paradox, the latter being a criticism of Quantum Mechanics. These later works were regarded even by physicists for decades as mere Gedanken or thought experiments. In recent years, not only have they been verified experimentally but revolutionary technological applications are emerging including quantum cryptography and possible quantum computing.

Precision Measurements of Fine and Hyperfine Structure in Lithium I and II PDF

W. A. van Wijngaarden, Canadian Journal of Physics, 83, 327-337 (2005)

Recent advances in modeling Li I and II in conjunction with improved experimental techniques have enabled precise tests of quantum electrodynamics. For Li⁺, the hyperfine intervals of the 1s2s ³S₁ and 1s2p ³P_0,1,2 states are in excellent agreement with theory. A recent measurement of the 1s2p ³P_1,2 fine structure interval also agrees well with the calculated value and resolves a discrepancy found by two prior experiments. For neutral lithium, discrepancies exist among the results of various experiments for the ^6,7Li D1 isotope shift and the 2P fine structure. However, all of the fine structure measurements are several MHz larger than the theoretical value. Prospects for future experiments to improve the determination of the fine structure constant and the relative ^6,7Li nuclear charge radii are discussed.

New Measurements of Absolute Total Cross Sections for Electron Impact on Cesium using a Magneto-Optical Trap PDF

M. Lukomski, J. MacAskill, D. Seccombe, C. McGratth, S. Sutton, J. Teeuwen, W. Kedzierski, T. Reddish, J. McConkey & W. A. van Wijngaarden, J. Phys. B, 38, 3535-3545 (2005)

A new magneto-optical trap (MOT) designed specifically for measurement of electron impact cross sections is described. Experimental results for electron impact total cross sections involving 62S ground state Cs are presented over the energy range 5-200 eV. Significant disagreement is obtained between our experimental data and Convergent Close Coupling (CCC) or Breit-Pauli R-Matrix calculations at the lower energies. Above 100 eV our data overlap earlier measurements from this laboratory made with a completely different apparatus and agree well with the CCC results. A comparison is made with other measurements made using more conventional techniques.

Precision Spectroscopy of Li I & II PDF

W. A. van Wijngaarden & G. Noble, Proc. of SPIE ICONO 6257, 14-16 (2005)

Advances in modeling lithium along with improved measurement have enabled precise tests of QED and allowed for the determination of nuclear radii. These are reviewed and prospects to improve the determination of the fine structure constant are discussed.

Examination of Discontinuities in Hourly Surface Humidity in Canada during 1953-2003 PDF

W. A. van Wijngaarden & L. A. Vincent, Journal of Geophysical Research, 110, D22102 (2005)

Hourly values of relative humidity recorded at 75 stations across Canada were closely examined. For each station, a best fit linear trend estimated the change during 1953-2003 and a statistical t test determined whether the trend was significant at the 5% level. Significant decreases in relative humidity are found throughout Canada in winter and spring. Fewer and weaker trends are observed during summer and fall. These results are in agreement with the changes observed in dew point, temperature and precipitation, at the same stations and over the same period of time. The data were also checked for possible discontinuities that could arise due to changes of procedures and instrumentation. The replacement of the pscychrometer by the dewcel has produced a decreasing step in winter relative humidity in the early 1970s at several stations experiencing very cold temperatures. This does not affect the observed trends in winter at southern and coastal locations.

Examination of Hourly Surface Pressure in Canada during 1953-2003 PDF

W. A. van Wijngaarden, International Journal of Climatology, 15, 2041-2049 (2005)

Hourly values of surface pressure recorded at 90 stations across Canada during 1953-2003 were examined. For each station, a linear trend was fitted to the data and a statistical t test determined whether the trend was significant at the 5% level. Most of the stations located above 60o N latitude reported a statistically significant decrease in winter pressure averaging -5.8 hPa over the 50 year period. This may be evidence for change in circulation patterns on decadal time scales due to the so called Arctic oscillation. Fewer and weaker statistically significant trends were found for these northern stations for the other seasons. Very few stations in southern Canada has significant trends in any season.

Bose Einstein Condensates of Dilute Alkali Vapours: A Coherent Ensemble of Atoms PDF

W. A. van Wijngaarden & B. Lu, Physics in Canada, 60, No. 5, 301-308 (2004)

Experiments involving Bose Einstein Condensates of dilute alkali vapours began less than a decade ago. Today a number of techniques enable condensates to be conveniently studied. An example is given of how to prepare a ⁸⁷Rb condensate in a QUIC trap composed of Quadrupole and Ioffe magnetic field coils. Novel applications of condensates are reviewed including atom interferometry, superfluidity, controlling the speed of light and the behaviour of a coherent array of condensates in an optical lattice. The latter have intriguing implications for quantum computing.

Bose Einstein Condensation in a QUIC Trap PDF

B. Lu & W. A. van Wijngaarden, Canadian Journal of Physics, 82, 81-102 (2004)

The apparatus and procedure required to generate a pure Bose-Einstein condensate (BEC) consisting of about half a million ⁸⁷Rb atoms at a temperature of 54 is described. The atoms are first laser cooled in a vapour cell magneto-optical trap (MOT) and subsequently transferred to an ultra-low pressure MOT. The atoms are loaded into a QUIC trap consisting of a pair of quadrupole coils and a Ioffe coil that generates a small finite magnetic field at the trap energy minimum to suppress Majorana transitions. Evaporation induced by an RF field lowers the temperature permitting the transition to BEC to be observed by monitoring the free expansion of the atoms after the trapping fields have been switched off.

An Axial Molecular Beam Diode Laser Spectrometer PDF

H. Osthoff, W. Jaeger, J. Walls & W. A. van Wijngaarden, Review of Scientific Instruments, 75, 46-53 (2004)

A mid-infrared tunable diode laser molecular beam spectrometer for the purpose of trace gas sensing and the study of van der Waals complexes id described. The spectrometer employs a Herriott multipass cell with up to 72 passes. The sample gas is injected parallel to the optical axis through a hole at the center of the far mirror. The molecular absorption is Doppler split, resulting form the laser beam propagating parallel and antiparallel to the molecular beam expansion. The axial expansion leads to narrower line widths and increased sensitivity, compared to the traditional vertical injection method, as a result of selective sampling of the central part of the molecular expansion with reduced Doppler broadening and longer residence time of the molecular sample in the laser beam. The molecular expansion leads also to selective signal enhancement of low J transitions, as demonstrated for the n₃ antisymmetric stretch vibration of CO₂. A microwave horn antenna was implemented into the spectrometer to enable microwave infrared double resonance experiments. The spectrometer performance was evaluated by recording spectra of the CO₂-Ar, (CO₂)₂, CO₂-He, and CO₂-SO₂ van der Waals complexes near the R(0) transition of the n₃ band of CO₂ around 2349 cm^-1. The feasibility of using a pulsed molecular expansion for trace gas sensing is explored.

Trends in Relative Humidity in Canada during 1953-2003 PDF

W. A. van Wijngaarden & L. A. Vincent, Bulletin of American Meteorological Soc., 85, 349 (2004)

Atomic, Molecular & Optical Physics: Physics 2000 Plus: Into the New Millenium PDF

W. A. van Wijngaarden, ed. G. Tibell & J. Ogborn, International Union of Pure & Applied Physics (2003)

Stark Shifts and Fine Structure of the ⁶Li 3D_3/2,5/2 States PDF

R. Ashby, J. J. Clarke & W. A. van Wijngaarden, European Physics Journal D, 23, 327-331 (2003)

The ⁶Li 3D_3/2,5/2 states were studied using a diode laser to first excite the 2P_3/2 state and a dye laser to populate the 3D_3/2,5/2 states. The dye laser was modulated by an electro-optic modulator and intersected an atomic beam that passed through a field free region and subsequently through a uniform electric field. A value of 1084.24 ± 0.20 MHz was found for the 3D fine structure splitting. The scalar and tensor polarizabilities were determined to be a_o(3D_5/2) = -3.772 ± 0.015, a₂(3D_3/2) = 2.893 ± 0.017, a_o(3D_5/2) = -3.772 ± 0.008 and a₂(3D_5/2) = 4.058 ± 0.013 MHz/(kV/cm)².

Precision Spectroscopy of Li I & II PDF

J. J. Clarke & W. A. van Wijngaarden, Recent Research Developments in Physics, 3, 347-378 (2003)

Recent advances in theory have renewed interest in precision measurements for 2 and 3 electron systems. This paper reviews measurements of the Li⁺ 1s2s ³S ® 1s2p ³P transition and the neutral lithium D lines. It also discusses a new technique where an electro-optically modulated laser beam is frequency scanned across the resonance of either an ion or neutral beam. The linearity of the laser scan is corrected by passing part of the laser beam through an etalon. The free spectral range of the etalon is separately calibrated for each scan using the electro-optic modulation frequency permitting important consistency checks. The results for the isotope shift, fine and hyperfine splittings are more accurate than previous experiments and resolve significant discrepancies in the literature.

Hyperfine and Fine Structure Measurements of ^6,7Li⁺ 1s2s 3S & 1s2p 3P States PDF

J. J. Clarke & W. A. van Wijngaarden, Physical Review A, 67, 12506, 1-5 (2003)

The 1s2s ³S₁ ® 1s2p ³P_1,2 transition in ^6,7Li⁺ was investigated by exciting a 5-6 keV ion beam with a nearly co-propagating ring-dye laser beam. The laser scan was calibrated using an electro-optic modulator to generate frequency sidebands. Results for the ⁶Li⁺ hyperfine splittings are an order of magnitude more precise than existing data in the literature and the ⁷Li⁺ results resolve an 11 MHz (17s) discrepancy for the ³P_1-2 fine structure interval as determined by two experiments. The results for 12 (all 13) measured hyperfine intervals in ^6,7Li⁺ are within 2s (3s) of the latest Hylleraas variational calculations.

Measurement of Isotope Shifts, Fine & Hyperfine Splittings in the Lithium D Lines PDF

J. Walls, J. J. Clarke & W. A. van Wijngaarden, European Physics Journal D, 22, 159-162 (2003)

The lithium D lines were studied using a diode laser that was frequency modulated by an electro-optic modulator, to excite an atomic beam. The transmission of part of the laser beam through an etalon was monitored to correct for the nonlinearity of the laser scan. The results for the ^6,7Li 2S_1/2 and 2P_1/2 hyperfine splittings agree very well with the best existing data while those for the D1 isotope shift and ^6,7Li fine structure splittings disagree significantly from data obtained by previous laser atomic beam experiment. Our result for the D1 isotope shift is very close to the latest value computed using Hylleraas Variational theory.

Lifetimes and Polarizabilities of Low Lying S, P and D States PDF

R. Ashby & W. A. van Wijngaarden, J. Quant. Spect. & Radiative Trasnfer, 76, 467-473 (2002)

The radiative lifetimes, scalar and tensor polarizabilities of low lying S, P and D states of lithium are obtained using a Coulomb approximation. The calculated lifetimes agree very well with the handful of experimental values listed in the literature. The ground state polarizability is also close to the measured result. This method requires substantially less computational time than ab initio theory, thereby permitting the study of nearly 40 states.

Axial Molecular Beam Diode Laser Spectrometer for Environmental Monitoring & the Study of Weakly Bound Complexes PDF

H. Osthoff, W. Jaeger, J. Walls & W. A. van Wijngaarden, Proc. SPIE, 4817, 249-257 (2002)

A novel molecular beam spectrometer for the purpose of trace gas sensing is described. Sensitivity is greatly enhanced and absorption interference by atmospheric H₂O and CO₂ is greatly reduced by using a molecular expansion. The expansion results in rotational cooling and population enhancement of low-lying energy levels. The instrument employs a tunable mid-infrared lead salt diode, which operate in single mode from 2348.5 to 2351.1 cm^-1, and a 36 m Herriott multipass cell. The sample gas is injected axially through a coupling hole in one of the spherical mirrors. The result is an increase of the residence time of the molecular beam in the sampling region. Pulsed operation of the nozzle allows background subtracted spectra to be acquired. The spectrometer can either by operated in fast scan mode, in which the laser frequency is rapidly scanned over the absorption feature of interest, or in frequency modulation mode with 2f-detection. A special adaptation of frequency modulation to the axial sampling system is described. Sample data of CO₂ are presented.

Electromagnetically Induced Transparency using a Vapour Cell & Laser Cooled Cs Atoms PDF

J. J. Clarke, W. A. van Wijngaarden & H. Chen, Physical Review A, 64, 023818 (2001)

Electromagnetically induced transparency was observed in a mismatched wavelength cascade system using a room temperature vapour cell and laser cooled atoms. A CW probe laser beam monitored the cesium 6S_1/2 → 6P_3/2 transition while another CW laser coupled the 6P_3/2 state to a higher excited state. The ratio of the observed Rabi frequencies for coupling to the 6P_3/2 → (11 – 13) D_3/2, _5/2 transitions agreed closely with that predicted using the transition oscillator strengths. A comparison of the EIT signals obtained using cold atoms and the vapour cell is made.

Precise Polarizabilities of Rubidium Excited States PDF

J. Walls, S. Cauchi, G. Karkas, J. Clarke, H. Chen & W. A. van Wijngaarden, European Physics Journal D, 14, 9-13 (2000)

Polarizabilities were determined by measuring stark shifts of transitions using an electro-optically modulated laser beam to excite an atomic beam. The voltage required for atoms excited by the laser beam in an electric field to be simultaneously in resonance as atoms excited by a frequency sideband of the laser in a field free region was measured. The scalar and polarizabilities were found to be: a₀(9S_1/2) = 103.77 ± 0.09, a₀(10S_1/2) = 272.54 ± 0.16, a₀(8D_3/2) = 230.68 ± 0.25 and a₂(8D_3/2) = 26.55 ± 0.10, a₀(8D_5/2) = 222.68 ± 0.14 and a₂(8D_5/2) = 51.91 ± 0.10 MHz/(kV/cm)². The results are 100 times more accurate than previous measurements and are within 1% of those found theoretically using a Coulomb approximation calculation.

Electromagnetically Induced Transparency & Optical Switching in a Rubidium Cascade System PDF

J. J. Clarke, H. Chen & W. A. van Wijngaarden, Applied Optics, 40, 2047-2051 (2000)

Electromagnetically induced transparency (EIT) is observed in a mismatched wavelengths cascade system using a room temperature rubidium vapour cell. A CW probe laser beam monitors the 5S_1/2 → 5P_3/2 transition while another CW laser couples the 5P_3/2 state to a higher excited state. The ratio of the observed Rabi frequencies for coupling to the 5P_3/2 → 8D_3/2,5/2 transitions agrees very well with that predicted using the transition oscillator strengths. Optical switching is demonstrated using a 40 mW coupling laser beam modulated up to 5 MHz as was recently proposed by H. Schmidt et al in Appl. Phys Lett. 76, 3173 (2000).

Precision Measurements of Polarizabilities PDF

W. A. van Wijngaarden & J. J. Clarke, Proc. International Conference on Atomic Physics (1998)

Substantial progress has occurred during the last decade to develop improved methods for determining atomic polarizabilities. We review work that has been done on ground states as well as the study of Stark shifts of transitions to excited states that have been made with a precision of parts in 10⁴. Measurements done on alkali atoms have yielded significantly more accurate data than previously available, stringently testing atomic theory.

Lifetimes & Polarizabilities of Low Lying S, P & D States of Francium PDF

W. A. van Wijngaarden & J. Xia, J. Quant. Spect. & Rad. Transfer, 61, No. 4, 557-561 (1998)

The lifetimes as well as the scalar and tensor polarizabilities are computed for over 60 low lying S, P and D states of francium using a Coulomb approximation. The result for the 7P_3/2 state lifetime agrees very closely with a recent measurement while the scalar polarizability of the ground state is estimated to be substantially lower than previously predicted. No other lifetime or polarizability determinations were found in the literature. This will facilitate future studies of francium spectroscopy.

Suppression of Majorana Transition in a Magnetic Trap using a Static Electric Field PDF

W. A. van Wijngaarden & J. J. Clarke, Canadian Journal of Physics, 76, No. 4, 305-310 (1998)

A neutral atom trap is proposed consisting of a magnetic field generated by a pair of anti-Helmholtz coils and a fringing electric field of a parallel plate capacitor. The electric field shifts the energy minimum of the trap away from the point where the magnetic field is zero thus preventing atom loss from the trap due to Majorana transitions. This trap offers some advantages over existing traps that are used to study cold atoms.

Precise Determination of Polarizabilities of Cesium (10-13)D_3/2,5/2 States PDF

J. Xia, J. J. Clarke, J. Li & W. A. van Wijngarden, Physical Review A, 56, No. 6, 5176-5178 (1997)

The scalar and tensor polarizabilities of the cesium (10-13)D_3/2,5/2 states were found with uncertainties of less than 0.3%. This experiment measured the voltage required for atoms excited by a laser beam in an electric field to be simultaneously in resonance as atoms excited by a frequency sideband of the laser in a field free region. The results are in reasonable agreement with theoretical calculations.

Elliptical Instability of the Earth’s Fluid Core PDF

K. Aldridge, B. Seyed-Mahmoud, G. Henderson & W. A. van Wijngaarden, Physics of Earth & Planetary Interactions, 103, 365-374 (1997)

The elliptical instability of a rotating fluid contained in a thick spherical shell has been excited in our laboratory by a tide-like perturbation of the flexible inner boundary. For an inviscid fluid, the growth of the instability is approximately proportional to the perturbation amplitude and the rotation rate. Development of the instability appears to be limited by the spherical outer surface and the relatively small perturbation applied over the inner surface. If the corresponding instability were excited in the Earth’s fluid core by tidal forces, in the absence of dissipation the e-folding time for growth would be on the order of several thousand years. Although this time scale is similar to current estimates for the time needed for the geomagnetic field to undergo a reversal, the instability would flow at a rate equal to the difference between the ideal growth rate and the overall decay rate. The rates of viscous and electromagnetic damping are determined by material properties of the core fluid that are not well known. If elliptical instability plays a central role in geomagnetic reversals, upper limits on the viscosity and conductivity of the fluid core might be inferred.

Calibration of Frequency Scan using an Electro-Optic Modulator PDF

W. A. van Wijngaarden & J. Li, Applied Optics, 36, No. 24, 5905-5907 (1997)

An electro-optically modulated laser beam was used to excite the Yb ¹S₀(6s)² → ³P₁(6s6p) transition. Fluorescence was recorded as the laser frequency was scanned across the transition. Each isotope generated multiple peaks in the spectrum separated by the modulation frequency that permitted the frequency scan to be calibrated. The resulting isotope shifts agree well with existing data obtained with an interferometer to monitor the change in laser frequency. Electro-optic modulators have the advantage of being relatively inexpensive and simpler to operate than interferometers whose length must typically be stabilized with a laser whose wavelength is locked to an atomic transition.

Precise Stark Shift Measurements using an Electro-optically Modulated Laser Beam PDF

W. A. van Wijngaarden & J. Li, Physical Review A, 55, No. 4, 2711-2715 (1997)

Stark shifts were determined using an electro-optically modulated laser beam. The voltage required for atoms excited by the laser beam in an electric field, to be simultaneously in resonance as atoms excited by a frequency sideband of the laser in a field free region, was measured. The scalar a₀ and tensor a₂ polarizabilities of the cesium 11D state were found to be a₀(11D_3/2) = -2694.6 ± 2.7, a₂(11D_3/2) = 2107.5 ± 2.7, a₀(11D_5/2) = -3379.5 ± 5.4 and a₂(11D_5/2) = 4242.1 ± 11.4 MHz/(kV/cm)². The tensor polarizabilities are the most accurate yet determined for any atomic states.

Scalar & Tensor Polarizabilities of Low Lying S, P, D, F & G States in Rubidium PDF

W. A. van Wijngaarden, J. Quant. Spect. & Rad. Trans., 57, No. 2, 275-279 (1997)

The scalar and tensor polarizabilities of over 50 of the lowest S, P, D, F and G states of Rubidium are evaluated using a Coulomb approximation. The computed results are in good agreement with measured values found in the literature which are briefly reviewed. The scalar polarizability a₀ of the (5-12)S_1/2 states is found to be given to within 2% by the formula a₀/n*⁷ = 0.267 + 8.69/n* where n* is the effective principal quantum number.

Precision Stark Shift Measurement of the (4s)^{2 1}S₀ – (4s4p) ³P₁ Transition in Calcium PDF

J. Li & W. A. van Wijngaarden, Phys. Rev. A, 53, No. 1, 604-606 (1996)

The Stark shift of the (4s)^{2 1}S₀ – (4s4p) ³P₁ transition in calcium was measured using a laser to excite an atomic beam as it traversed through a uniform electric field and a field-free region. The laser frequency was scanned across the transition, while fluorescence produced by the radiative decay of the excited state was detected. The frequency scan was calibrated using an acousto-optic modulator to frequency shift part of the laser beam. The Stark shift rate was found to be -12.314 ± 0.041 kHz/(kV/cm)², where the minus sign indicates the transition frequency decreases when the electric field is applied.

Precision Spectroscopy using Acousto-Optic Modulators PDF

W. A. van Wijngaarden, Advances in Atomic, Molecular & Optical Physics, (B. Bederson & H. Walter, Eds.) Academic press, San Diego, 36, 141-182 (1996)

Precision optical spectroscopy is an invaluable tool to study atomic structure. Absolute measurements of optical transition frequencies can be readily made with an accuracy of parts in 10⁹ [Riis et al, 1994]. However, in many experiments one is primarily interested in determining the energy interval separating two nearby states. Examples include: fine and hyperfine structure splittings, isotope shifts and the Lamb shift. Additional frequency shifts arise when electric and magnetic fields are applied to the atom. These energy splittings can be found by subtracting precisely determined frequencies of transitions occurring to the states in question. For example, consider an atom that has an optical transition at 5×10¹⁴ Hz to an excited state consisting of two hyperfine levels separated by 1 GHz. The hyperfine splitting can be determined with an uncertainty of 1 MHz if the transition frequencies to the two hyperfine levels are measured with accuracies of one part in 5×10⁸. A different approach is to measure the hyperfine splitting directly which only requires a measurement accurate to one part in 10³. The latter task requires simpler and cheaper apparatus and is therefore in general easier.

Hyperfine Splitting and Isotope Shifts of (6s)^{2 1}S₀– (6s6p) ¹P₁ Transition in Barium PDF

W. A. van Wijngaarden & J. Li, Canadian Journal of Physics, 73, 484-488 (1995)

The hyperfine and isotope shifts of the (6s)^{2 1}S₀ – (6s6p) ¹P₁ transition in barium were measured using a ring dye laser to excite an atomic beam. The laser frequency was scanned across the transition while fluorescence produced by the radiative decay of the state was detected. The frequency was calibrated using an acousto-optic modulator to frequency shift part of the laser beam. The spectrum therefore consisted of pairs of peaks separated by the modulation frequency. The shifts (MHz) relative to ¹³⁸Ba are ¹³⁷Ba F = 5/2, 63.43 ± 0.25; ¹³⁵Ba F = 5/2, 120.55 ± 0.25; ¹³⁶Ba, 128.02 ± 0.39; ¹³⁷Ba F = 3/2, 274.56 ± 0.09; ¹³⁵Ba, 323.44 ± 0.19; and ^135,137Ba F = 1/2, 549.47 ± 0.12 where the transition in ¹³⁸Ba occurs at the lower frequency. The magnetic dipole A and electric quadrupole B hyperfine coupling constants (MHz) of the (6s6p) ¹P₁ state were determined to be A(¹³⁵Ba) = -98.16 ± 0.14, B(¹³⁵Ba) = 34.01 ± 0.22, A(¹³⁷Ba) = -109.50 ± 0.13, and B(¹³⁷Ba) = 50.09 ± 0.21.

Measurements of Stark Shift of (6s)^{2 1}S₀ – (6s6p) ¹P₁ Transition in Barium PDF

J. Li & W. A. van Wijngaarden, Physical Review A, 51, No. 5, 3560-3563 (1995)

The Stark shift of the (6s)^{2 1}S₀ – (6s6p)¹P₁ transition in barium was measured using a laser to excite an atomic beam as it traversed a uniform electric field and a field free region. The laser frequency was scanned across the transition while fluorescence produced by the radiative decay of the excited state was detected. The frequency scan was calibrated using an acousto-optic modulator which frequency shifted the laser by a specified amount. The Stark shift rate was found to be -28.532 ± 0.060 kHz/(kV/cm)². The hyperfine splitting of the ^135,137Ba F = 1/2 level relative to ¹³⁸Ba of the (6s6p)¹P₁ state was determined to be -549.47 ± 0.12 MHz where the minus sign indicates that the ¹³⁸Ba transition is at lower frequency.

Measurements of Stark Shift of (6s)^{2 1}S₀ – (6s6p) ³P₁ Transition in Ytterbium PDF

W. A. van Wijngaarden & J. Li, Journal of Physics B, 28, 2559-2563 (1995)

The Stark shift of the (6s)^{2 1}S₀ – (6s6p) ³P₁ transition in ytterbium was measured using a laser to excite an atomic beam first in a uniform electric field and subsequently in a field free region. The laser frequency was scanned across the transition while fluorescence produced by the radiative decay of the excited state was detected. The frequency scan was calibrated using isotope and hyperfine splittings that have been measured previously. The Stark shift rate was found to be -15.419 ± 0.048 kHz/(kV/cm)² and the tensor polarizability of the (6s6p) ³P₁ state was determined to be a₂ = 5.81 ± 0.13 kHz/(kV/cm)².

Measurement of Na 3P_{1/2. 3/2} Isotope Shifts and Hyperfine Structure PDF

W. A. van Wijngaarden & J. Li, Zeitschrift fur Physik D, 32, 67-72 (1994)

The hyperfine levels of the sodium 3P_1/2,3/2 states were resolved using a narrow linewidth laser to excite the ground state. The laser frequency was scanned while fluorescence resulting from the radiative decay of the excited states was detected. The frequency was calibrated using the known hyperfine splitting of the ground state. The magnetic dipole A and electric quadrupole B hyperfine coupling constants of the excited states were determined to be A(3P_1/2) = 94.44 ± 0.13, A(3P_3/2) = 18.62 ± 0.21 and B(3P_3/2) = 2.11 ± 0.52 MHz. The uncertainty of A(3P_1/2) is less than results previously reported while the data for the 3P_3/2 state are consistent with those existing in the literature

Measurement of Yb Isotope Shifts & Hyperfine Splittings using Acoust-Optic Modulation PDF

W. A. van Wijngaarden & J. Li, Journal Optical Society of America B, 11, No. 11, 2163-2166 (1994)

The isotope and hyperfine shifts for the Yb ¹S₀(6s²) – ³P₁(6s6p) transition were determined with an acousto-optic modulator used to frequency shift part of a laser beam. The frequency-shifted and unshifted laser beams were superimposed and excited an atomic beam. The laser was scanned across the the transition while fluorescence produced by the radiative decay of the excited state was detected by a photomultiplier. Each isotope generated two peaks in the spectrum separated by the acousto-optic shift, which permitted the frequency to be calibrated. This relatively simple method yields results that agree well with the most accurate existing data, which were obtained by measurements of frequency shift with a Fabry Perot etalon whose length was stabilized with a helium-neon laser locked to an iodine line.

Calculated Polarizabilities of Cesium S, P, D and F States PDF

W. A. van Wijngaarden & J. Li, J. Quant. Spect. & Rad. Trans., 52, No. 5, 555-562 (1994)

The scalar and tensor polarizabilities of over sixty S, P, D and F states of cesium are evaluated using a Coulomb approximation. The expected scaling of polarizabilities as n*⁷, where n* is the effective principle quantum number, was found to hold well for the higher excited states. The computed results agree closely with experimental measurements which are reviewed.

Precision Measurements of Stark Shifts for 6P_3/2 – nS_1/2 n=10-13 Transitions in Cesium PDF

W. A. van Wijngaarden, E. A. Hessels, J. Li & N. E. Rothery, Physical Review A, 49, No. 4, R2220-R2223 (1994)

The Stark shifts of four transitions in cesium were measured using two atomic beams. One traverses through a uniform electric field and the other a field free region. The atoms were excited using a ring dye laser, with the laser beam interacting with the atoms in the electric field region frequency shifted by an acousto-optic modulator. The Stark shift was determined by measuring the electric field for which the atoms in both beams are simultaneously in resonance. The results for the 6P_3/2→(10-13)S_1/2 transitions are -59.36(14), -154.68(13), -356.57(29) and -745.43(61) MHz (kV/cm)², respectively.

Laser Isotope Separation of Barium using an Inhomogeneous Magnetic Field PDF

W. A. van Wijngaarden & J. Li, Physical Review A, 49, No. 2, 1158-1164 (1994)

A barium atomic beam undergoes selective isotope excitation by a dye laser to the ¹P₁ state. This state radiatively decays back to the ground state or to the (6s5d)D states, which are deflected out of the beam by an inhomogeneous magnetic field. The residual atomic beam is examined by a quadrupole mass spectrometer, and isotopic depletions of up to 60% are obtained using laser powers of a few hundred milliwatts. The isotopic splitting of the ¹S₀ – ¹P₁ transitions for ¹³⁶Ba and the F = 5/2 states of ^135,137Ba are measured relative to that for ¹³⁸Ba and agree well with those found previously.

Hyperfine Interaction Constants of the 8D_3/2 State in ⁸⁵Rb using Quantum Beat Spectroscopy PDF

W. A. van Wijngaarden, J. Li & J. Koh, Physical Review A 48, No. 1, 829-831 (1993)

Quantum beats due to the hyperfine interaction were observed in the radiative decay of the 8D3/2 state in Rb. The data agree well with theory allowing determination of the magnetic dipole (|a|=0.879 ± 0.008 MHz) and electric quadrupole |b|= 0.15 ± 0.02 MHz) (a/b>0) hyperfine constants. The results are consistent with those obtained for other D states in ⁸⁵Rb and ⁸⁷Rb. The observed magnetic dipole constants for the nD3/2, n>7 states of ⁸⁵Rb are given to within 2% by the relation a(MHz) = 252/ n*³ where n* is the effective principal quantum number.

Lifetime Measurements of Rubidium nD_3/2 (n=6-9) States using the Hanle Effect PDF

W. A. van Wijngaarden & J. Sagle, Physical Review A 45, No. 3, 1502-1508 (1992)

A Hanle experiment has been used to determine the following radiative lifetimes (in nsec) of rubidium: τ(6D3/2) = 298 ± 8, τ(7D3/2) = 345 ±9, τ(8D3/2) = 586 ± 15, τ(9D3/2) = 638 ± 17. These data were taken at a temperature of 293 K and are not corrected for effects due to blackbody radiation. The effect of the hyperfine interaction on the Hanle signal is discussed in detail for an excited state of arbitrary angular momentum.

Excited State Hyperfine Structure in ¹³³Cs using Quantum Beat Spectroscopy PDF

J. Sagle & W. A. van Wijngaarden, Canadian Journal of Physics 69, No. 7, 808-812 (1991)

Quantum beats arising from the hyperfine interaction were observed in the fluorescence produced when the 8D_3/2, 9D_3/2 and 10D_3/2 states of ¹³³Cs radiatively decayed to the 6P_1/2 state. The period of the beats equals the reciprocal of the magnetic dipole coupling constant a since the ¹³³Cs nucleus has a negligibly small electric quadrupole moment. The results are a = 3.95 ± 0.01, 2.38 ± 0.01 and 1.54 ± 0.02 MHz for the 8D_3/2, 9D_3/2 and 10D_3/2 states, respectively.

Magnetic Field Decoupling of an Alkali Metal Excited State Hyperfine Structure PDF

W. A. van Wijngaarden & J. Sagle, Physical Review A 43, No. 5, 2171-2178 (1991)

The theory of how excited state hyperfine structure can be determined using a magnetic field to decouple the nuclear and electronic angular momentum is presented. The initial excite state is assumed to have an anisotropic Zeeman sublevel population distribution, which can be conveniently created by a laser induced multiphoton excitation of an unpolarized atom. The Zeeman sublevel populations are subsequently mixed by the hyperfine interaction. The degree of mixing is controlled by a magnetic field applied along the quantization axis. The relative Zeeman sublevel populations can be monitored by detecting the polarization of fluorescence emitted when the excited state radiatively decays. It is convenient to take the ratio of two time integrated fluorescent signals measured for orthogonal linear polarizations, since this is independent of the excited state number density. The plot of this ratio versus magnetic field is very well approximated by a Lorentzian curve whose halfwidth is proportional to the magnetic dipole hyperfine coupling constant. This method was used to determine the magnitude of the magnetic dipole constant of the cesium 8D_3/2 state to be 3.92 ± 0.10 MHz, which is in excellent agreement with previous results.

Hyperfine Structure of Excited Alkali States using Quantum Beat Spectroscopy PDF

W. A. van Wijngaarden & J. Sagle, Journal of Physics B 24, 897-903 (1991)

Quantum beats arising from the hyperfine interaction were observed in the 7D_3/2 → 5P_1/2 transition in ⁸⁵Rb. Theoretical expressions for the beat signals were fitted to the data to determine the magnetic dipole constants a = 1.415 ± 0.030 MHz, electric quadrupole constant b = 0.31 ± 0.06 MHz and the radiative lifetime τ = 346 ± 25 nsec of the ⁸⁵Rb 7D_3/2 state.

Theory of the Inverse Hook Method for Measuring Oscillator Strengths PDF

W. A. van Wijngaarden, K. D. Bonin & W. Happer, Physical Review A 36, No. 3, 1187-1199 (1987)

The theory of a new method to measure oscillator strengths is presented. The method exploits the ac Stark interaction of a laser pulse detuned from a transition between an initially populated states a and a second state b of an atom. We assume the density matrix rho of state a initially has only diagonal elements given by = C + Dm² where C and D ≠ 0 are constants and m is the Zeeman sublevel quantum number. The laser pulse is linearly polarized along an axis different from the quantization axis and therefore rearranges the atoms among the various Zeeman sublevels. Changes of the relative Zeeman sublevel populations induced by the laser pulse can be readily detected by monitoring changes in the angular distribution or polarization of fluorescent light emitted when the atoms radiatively decay to some final state f. This paper considers the general problem where states a, b, and f have arbitrary angular momentum. We derive the functional dependence of the polarized fluorescent light fluence on the laser pulse fluence (pulse energy per unit area). For spatially uniform laser pulses, these signals are periodic functions of the laser fluence. When the laser is completely speckled, we show that the signal is well approximated by a Lorentzian curve. This latter case is of considerable experimental interest since most pulsed dye lasers have poor transverse mode structure which can readily be converted into a statistically well defined speckle pattern. The oscillator strength of the transition between states and and b is found using (1) the fluence halfwidth of the “depolarization curve”, the lorentzian like dependence of the fluorescence polarization on the laser pulse fluence, (2) the detuning of the laser from the transition frequency ω_ab and (3) some known constant factors which depend on the angular momenta of the states a, b, and f. The physics of the situation is very similar to that of the conventional hook method with this difference: the roles of the atoms and the photons have been interchanged. We therefore call this new method the inverse hook method. The inverse hook method is relatively insensitive to the details of the atomic absorption line shape and also to the temporal and spatial profile of the laser pulse. it yields absolute oscillator strengths and it is especially suitable for measurements of transitions between excited atomic states, including autoionizing states.

The Inverse Hook Method for Measuring Oscillator Strengths

W. A. van Wijngaarden, K. D. Bonin & W. Happer, Laser Spectroscopy VIII, edited by W. Persson & S. Svanberg, Are, Sweden, 406 (1987)

An Optical Pumping Primer PDF

W. Happer & W. A. van Wijngaarden, Journal of Hyperfine Interactions 38, 435,470 (1987)

This pedagogical paper introduces the basic ideas of optical pumping. Some of the various optical pumping mechanisms are discussed, and illustrated by diagrams showing the experimental apparatus. The density matrix formalism is introduced and used to quantitatively examine the effects of optical pumping. Next, some of the various spin relaxation mechanism such as collisions and spin exchange between electrons and nuclei are discussed. A good knowledge of elementary quantum mechanics is needed to follow the article.

Inverse Hook Method for Measuring Oscillator Strengths PDF

W. A. van Wijngaarden, K. D. Bonin & W. Happer, Journal of Hyperfine Interactions 38, 471-498 (1987)

We describe an effective new method to measure the oscillator strengths for transitions between the excited states of atoms. The oscillator strength is determined by measuring changes in the angular distribution or polarization pf fluorescent light emitted by atoms in the initial or final state of the transition of interest, after these atoms have been subject to the a.c. Stark shift of an off-resonant laser pulse. The physics of the situation is very similar to that of the conventional hook method with this difference: the roles of the atoms and the photons have been interchanged. We therefore call this new method the inverse hook method. The inverse hook method is relatively insensitive to the details of the atomic absorption lineshape and also to the temporal and spectral profile of the laser pulse. It yields absolute oscillator strengths and it is especially suitable for measurements of transitions between excited atomic states, including autoionizing states.

The Inverse Hook Method for Measuring Oscillator Strengths

W. A. van Wijngaarden, PhD Thesis, Princeton (1986)

Inverse Hook Method for Measuring Oscillator Strengths PDF

W. A. van Wijngaarden, K. D. Bonin, W. Happer, E. Miron, D. Schreiber & T. Arisawa, Physical Review Letters 56, No. 19, 2024-2027 (1986)

We describe a new method for measuring oscillator strengths for transitions between excited atomic states. The oscillator strength is determined form changes in the angular distribution or polarization of fluorescent light induced by the ac Stark effect of a laser pulse. The method can be thought of as a variant of the hook method in which the roles of atoms and photons have been interchanged.

Observation of Quantum Beats in the 6D_3/2 – 5P_1/2 Transition in ⁸⁵Rb PDF

W. A. van Wijngaarden, K. D. Bonin & W. Happer, Physical Review A 33, No. 1, 77-81 (1986)

Quantum beats due to the hyperfine interaction were observed in the 6D_3/2→ 5P_1/2 transition in ⁸⁵Rb. Good agreement with theory was obtained, allowing determination of the values for the magnetic dipole (a = 2.32 ± 0.06 MHz) and electric quadrupole (b=1.62 ± 0.06 MHz) hyperfine constants for the upper state.

Polarization of the Nuclear Spins of Noble Gas Atoms by Spin Exchange with Optically Pumped Alkali Atoms PDF

W. Happer, E. Miron, S. Schaefer, D. Schreiber, W. A. van Wijngaarden & X. Zeng, Physical Review A 29, No. 6, 3092-3110 (1984)

The theory of spin exchange between optically pumped alkali metal atoms and noble gas nuclei is presented. Spin exchange with heavy noble gases is dominated by interactions in long lived van der Waals molecules. The main spin interactions are assumed to be the spin rotation interactions γ N.S between the rotational angular momentum N of the alkali metal-noble gas pair and the electron spin S of the alkali metal atom, and the contact hyperfine interaction α K.S between the nuclear spin K of the noble gas atom and the electron spin S. Arbitrary values for K and for the nuclear spin I of the alkali metal atom are assumed. Precise formal expressions for spin transfer coefficients are given along with convenient approximations based on a perturbation expansion in powers of (α/γN)² a quantity which has been shown to be small by experiment.

Wall Relaxation of Spin Polarized ¹²⁹Xe Nuclei PDF

X. Zeng, E. Miron, W. A. van Wijngaarden, D. Schreiber & W. Happer, Physics Letters 96A, 191-194 (1983)

The wall relaxation of spin polarized ¹²⁹Xe nuclei is much longer in silicone-coated pyrex cells than in uncoated cells. In contrast to uncoated glass cells where the wall relaxation times are unpredictable and usually only a few tens of seconds, the relaxation time of ¹²⁹Xe in silicone-coated cells is usually 20 minutes or longer.

Dissociative Excitation of SO₂ by Controlled Electron Impact PDF

K. Becker, W. A. van Wijngaarden & J. W. McConkey, Planetary Space Science 31, No. 2, 197-206 (1983)

The fragmentation of SO₂ following dissociative electron impact excitation has been studied under single collision conditions for incident electron energies up to 500 eV. The emission spectrum in the far v.u.v. spectral range (450 -1100 A) shows many features arising from excited neutral oxygen and ionized oxygen and sulphur fragments. Absolute emission cross sections have been measured for the most intense lines and the maximum values were found to range from 1-12 x 10^-19 cm² with an uncertainty of approximately ±35%. Dissociation mechanisms are discussed and in some cases the dissociation path could be uniquely identified. The striking differences between the v.u.v. emission spectrum produced by single step dissociation of SO₂ and the spectra emitted by the plasma torus around Jupiter are discussed.