Practical speed meter designs for quantum nondemolition gravitational-wave interferometers

In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors (e.g., LIGO-III and EURO), one strategy is to monitor the relative momentum or speed of the test-mass mirrors, rather than monitoring their relative position. A previous paper analyzed a straightforward but impractical design for a speed-meter interferometer that accomplishes this. This paper describes some practical variants of speed-meter interferometers. Like the original interferometric speed meter, these designs in principle can beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies. These variants essentially consist of a Michelson interferometer plus an extra ``sloshing'' cavity that sends the signal back into the interferometer with opposite phase shift, thereby cancelling the position information and leaving a net phase shift proportional to the relative velocity. In practice, the sensitivity of these variants will be limited by the maximum light power W-circ circulating in the arm cavities that the mirrors can support and by the leakage of vacuum into the optical train at dissipation points. In the absence of dissipation and with squeezed vacuum (power squeeze factor e(-2R)similar or equal to0.1) inserted into the output port so as to keep the circulating power down, the SQL can be beat by h/h(SQL)similar torootW(circ)(SQL)e(-2R)/W-circ at all frequencies below some chosen f(opt)similar or equal to100 Hz. Here W(circ)(SQL)similar or equal to800 kW(f(opt)/100 Hz)(3) is the power required to reach the SQL in the absence of squeezing. (However, as the power increases in this expression, the speed meter becomes more narrow band; additional power and reoptimization of some parameters are required to maintain the wide band. See Sec. III B.) Estimates are given of the amount by which vacuum leakage at dissipation points will debilitate this sensitivity (see Fig. 12); these losses are 10% or less over most of the frequency range of interest (fgreater than or similar to10 Hz). The sensitivity can be improved, particularly at high freqencies, by using frequency-dependent homodyne detection, which unfortunately requires two 4-km-long filter cavities (see Fig. 4)

An analysis of a QND speed-meter interferometer

In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors (e.g. LIGO-III and EURO), one strategy is to monitor the relative momentum or speed of the test-mass mirrors, rather than monitoring their relative position. This paper describes and analyzes the most straightforward design for a {\it speed meter interferometer} that accomplishes this -- a design (due to Braginsky, Gorodetsky, Khalili and Thorne) that is analogous to a microwave-cavity speed meter conceived by Braginsky and Khalili. A mathematical mapping between the microwave speed meter and the optical interferometric speed meter is developed and is used to show (in accord with the speed being a Quantum Nondemolition [QND] observable) that {\it in principle} the interferometric speed meter can beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies, and can do so without the use of squeezed vacuum or any auxiliary filter cavities at the interferometer's input or output. However, {\it in practice}, to reach or beat the SQL, this specific speed meter requires exorbitantly high input light power. The physical reason for this is explored, along with other issues such as constraints on performance due to optical dissipation. This analysis forms a foundation for ongoing attempts to develop a more practical variant of an interferometric speed meter and to combine the speed meter concept with other ideas to yield a promising LIGO-III/EURO interferometer design that entails low laser power.Comment: 12 pages, 5 figures; corrected formula and some values describing power requirement

A Pooled Analysis of Body Mass Index and Mortality among African Americans

Pooled analyses among whites and East Asians have demonstrated positive associations between all-cause mortality and body mass index (BMI), but studies of African Americans have yielded less consistent results. We examined the association between BMI and all-cause mortality in a sample of African Americans pooled from seven prospective cohort studies: NIH-AARP, 1995–2009; Adventist Health Study 2, 2002–2008; Black Women's Health Study, 1995–2009; Cancer Prevention Study II, 1982–2008; Multiethnic Cohort Study, 1993–2007; Prostate, Lung, Colorectal and Ovarian Screening Trial, 1993–2009; Southern Community Cohort Study, 2002–2009. 239,526 African Americans (including 100,175 never smokers without baseline heart disease, stroke, or cancer), age 30–104 (mean 52) and 71% female, were followed up to 26.5 years (mean 11.7). Hazard ratios (HR) and 95% confidence intervals (CI) for mortality were derived from multivariate Cox proportional hazards models. Among healthy, never smokers (11,386 deaths), HRs (CI) for BMI 25–27.4, 27.5–29.9, 30–34.9, 35–39.9, 40–49.9, and 50–60 kg/m2 were 1.02 (0.92–1.12), 1.06 (0.95–1.18), 1.32 (1.18–1.47), 1.54 (1.29–1.83), 1.93 (1.46–2.56), and 1.93 (0.80–4.69), respectively among men and 1.06 (0.99–1.15), 1.15 (1.06–1.25), 1.24 (1.15–1.34), 1.58 (1.43–1.74), 1.80 (1.60–2.02), and 2.31 (1.74–3.07) respectively among women (reference category 22.5–24.9). HRs were highest among those with the highest educational attainment, longest follow-up, and for cardiovascular disease mortality. Obesity was associated with a higher risk of mortality in African Americans, similar to that observed in pooled analyses of whites and East Asians. This study provides compelling evidence to support public health efforts to prevent excess weight gain and obesity in African Americans

Circulating 25-Hydroxyvitamin D and the Risk of Rarer Cancers: Design and Methods of the Cohort Consortium Vitamin D Pooling Project of Rarer Cancers

The Cohort Consortium Vitamin D Pooling Project of Rarer Cancers (VDPP), a consortium of 10 prospective cohort studies from the United States, Finland, and China, was formed to examine the associations between circulating 25-hydroxyvitamin D (25(OH)D) concentrations and the risk of rarer cancers. Cases (total n = 5,491) included incident primary endometrial (n = 830), kidney (n = 775), ovarian (n = 516), pancreatic (n = 952), and upper gastrointestinal tract (n = 1,065) cancers and non-Hodgkin lymphoma (n = 1,353) diagnosed in the participating cohorts. At least 1 control was matched to each case on age, date of blood collection (1974–2006), sex, and race/ethnicity (n = 6,714). Covariate data were obtained from each cohort in a standardized manner. The majority of the serum or plasma samples were assayed in a central laboratory using a direct, competitive chemiluminescence immunoassay on the DiaSorin LIAISON platform (DiaSorin, Inc., Stillwater, Minnesota). Masked quality control samples included serum standards from the US National Institute of Standards and Technology. Conditional logistic regression analyses were conducted using clinically defined cutpoints, with 50–<75 nmol/L as the reference category. Meta-analyses were also conducted using inverse-variance weights in random-effects models. This consortium approach permits estimation of the association between 25(OH)D and several rarer cancers with high accuracy and precision across a wide range of 25(OH)D concentrations

Association between Class III Obesity (BMI of 40–59 kg/m2) and Mortality: A Pooled Analysis of 20 Prospective Studies

Background: The prevalence of class III obesity (body mass index [BMI]≥40 kg/m2) has increased dramatically in several countries and currently affects 6% of adults in the US, with uncertain impact on the risks of illness and death. Using data from a large pooled study, we evaluated the risk of death, overall and due to a wide range of causes, and years of life expectancy lost associated with class III obesity. Methods and Findings: In a pooled analysis of 20 prospective studies from the United States, Sweden, and Australia, we estimated sex- and age-adjusted total and cause-specific mortality rates (deaths per 100,000 persons per year) and multivariable-adjusted hazard ratios for adults, aged 19–83 y at baseline, classified as obese class III (BMI 40.0–59.9 kg/m2) compared with those classified as normal weight (BMI 18.5–24.9 kg/m2). Participants reporting ever smoking cigarettes or a history of chronic disease (heart disease, cancer, stroke, or emphysema) on baseline questionnaires were excluded. Among 9,564 class III obesity participants, mortality rates were 856.0 in men and 663.0 in women during the study period (1976–2009). Among 304,011 normal-weight participants, rates were 346.7 and 280.5 in men and women, respectively. Deaths from heart disease contributed largely to the excess rates in the class III obesity group (rate differences = 238.9 and 132.8 in men and women, respectively), followed by deaths from cancer (rate differences = 36.7 and 62.3 in men and women, respectively) and diabetes (rate differences = 51.2 and 29.2 in men and women, respectively). Within the class III obesity range, multivariable-adjusted hazard ratios for total deaths and deaths due to heart disease, cancer, diabetes, nephritis/nephrotic syndrome/nephrosis, chronic lower respiratory disease, and influenza/pneumonia increased with increasing BMI. Compared with normal-weight BMI, a BMI of 40–44.9, 45–49.9, 50–54.9, and 55–59.9 kg/m2 was associated with an estimated 6.5 (95% CI: 5.7–7.3), 8.9 (95% CI: 7.4–10.4), 9.8 (95% CI: 7.4–12.2), and 13.7 (95% CI: 10.5–16.9) y of life lost. A limitation was that BMI was mainly ascertained by self-report. Conclusions: Class III obesity is associated with substantially elevated rates of total mortality, with most of the excess deaths due to heart disease, cancer, and diabetes, and major reductions in life expectancy compared with normal weight. Please see later in the article for the Editors' Summar