Improved Limits on the Coupling of Ultralight Bosonic Dark Matter to Photons from Optical Atomic Clock Comparisons.

We present improved constraints on the coupling of ultralight bosonic dark matter to photons based on long-term measurements of two optical frequency ratios. In these optical clock comparisons, we relate the frequency of the ^{2}S_{1/2}(F=0)↔^{2}F_{7/2}(F=3) electric-octupole (E3) transition in ^{171}Yb^{+} to that of the ^{2}S_{1/2}(F=0)↔^{2}D_{3/2}(F=2) electric-quadrupole (E2) transition of the same ion, and to that of the ^{1}S_{0}↔^{3}P_{0} transition in ^{87}Sr. Measurements of the first frequency ratio ν_{E3}/ν_{E2} are performed via interleaved interrogation of both transitions in a single ion. The comparison of the single-ion clock based on the E3 transition with a strontium optical lattice clock yields the second frequency ratio ν_{E3}/ν_{Sr}. By constraining oscillations of the fine-structure constant α with these measurement results, we improve existing bounds on the scalar coupling d_{e} of ultralight dark matter to photons for dark matter masses in the range of about (10^{-24}-10^{-17}) eV/c^{2}. These results constitute an improvement by more than an order of magnitude over previous investigations for most of this range. We also use the repeated measurements of ν_{E3}/ν_{E2} to improve existing limits on a linear temporal drift of α and its coupling to gravity.

Evaluation of a

We report on an evaluation of an optical clock that uses the ^{2}S_{1/2}→^{2}D_{5/2} transition of a single ^{88}Sr^{+} ion as the reference. In contrast to previous work, we estimate the effective temperature of the blackbody radiation that shifts the reference transition directly during operation from the corresponding frequency shift and the well-characterized sensitivity to thermal radiation. We measure the clock output frequency against an independent ^{171}Yb^{+} ion clock, based on the ^{2}S_{1/2}(F=0)→^{2}F_{7/2}(F=3) electric octupole (E3) transition, and determine the frequency ratio with a total fractional uncertainty of 2.3×10^{-17}. Relying on a previous measurement of the ^{171}Yb^{+} (E3) clock frequency, we find the absolute frequency of the ^{88}Sr^{+} clock transition to be 444 779 044 095 485.277(59) Hz. Our result reduces the uncertainty by a factor of 3 compared with the previously most accurate measurement and may help to resolve so far inconsistent determinations of this value. We also show that for three simultaneously interrogated ^{88}Sr^{+} ions, the increased number causes the expected improvement of the short-term frequency instability of the optical clock without degrading its systematic uncertainty.

[Models for determining optimal nutrition in private households]. / Modelle zur Bestimmung einer optimalen Ernährung in privaten Haushalten.

Members of private households have different nutrient requirements. In general, they eat the same dishes in different quantities. The menu plan is admissible if it corresponds to the recommended dietary allowances. It is acceptable if it meets the eating habits. It is optimal if it meets the constraints mentioned and best reaches an objective. It is the aim of this paper to describe models for the determination of optimal nutrition and to evaluate them with respect to their suitability for solving decision problems in private, multi-person-households. The fewer the model-intern restrictions in the variability of quantities of food stuffs, kind and/or quantities of dishes, the better are the "optimal" solutions that are found with the model. A simultaneous determination of kind and quantity of dishes reaches the model purpose better than a stepwise determination. This is shown in an example problem.

[Comparison of dietary surveys in Germany and Great Britain regarding objectives, methodology and results]. / Vergleich von Verzehrserhebungen in Deutschland und Grossbritannien nach Zielen, Methodik und Ergebnissen.

Referring to the data of the National Food Consumption Study in Germany and the Dietary and Nutritional Survey of British Adults, this article compares the food intake of German and British adults. Such a comparison is possible because both studies have mainly the same methodology. The comparison of the food intake of German and British adults points out food groups which Germans consume in higher amounts than British people do. To this category belong meat products and sausages, eggs, cheese and cottage cheese, butter, fat for cooking and salad oil, bread and pastries, vegetables, fruit, preserves and soft drinks. The Germans consume less meat, fish and fish products, milk and milk products, pasta, rice and miscellaneous cereals, potatoes, sugar, sweets and tea than the British people do. The consumption of fruit products, alcoholic beverages and coffee is nearly the same in Germany and Great Britain.