Terrestrial vs. spaceborne, quantum vs. classical tests of the equivalence principle

The equivalence principle can be tested by precision experiments based on classical and quantum systems, on the ground as well as in space. In many models, these tests are mostly equivalent in their ability to constrain physics beyond the Standard Model. We mention differences that nevertheless exist between spaceborne and quantum mechanical tests and their conventional competitors.Comment: Four pages for the proceedings of the sixth meeting on CPT and Lorentz symmetr

Matter-wave Tests of the Gravitational Redshift in Space

A recent measurement of the gravitational redshift was based on interference of matter waves. Operation in microgravity can improve it by a factor of $10^5$ and, in some models, even $10^{10}$.Comment: Talk given at the Fifth Meeting on CPT and Lorentz Symmetry, at Indiana University, Bloomington, IN. Corrected problem with Figur

Atom interferometry in an optical cavity

We propose and demonstrate a new scheme for atom interferometry, using light pulses inside an optical cavity as matter wave beamsplitters. The cavity provides power enhancement, spatial filtering, and a precise beam geometry, enabling new techniques such as low power beamsplitters ($<100 \mathrm{\mu W}$), large momentum transfer beamsplitters with modest power, or new self-aligned interferometer geometries utilizing the transverse modes of the optical cavity. As a first demonstration, we obtain Ramsey-Raman fringes with $>75\%$ contrast and measure the acceleration due to gravity, $\mathit{g}$, to $60 \mathrm{\mu \mathit{g} / \sqrt{Hz}}$ resolution in a Mach-Zehnder geometry. We use $>10^7$ cesium atoms in the compact mode volume ($600 \mathrm{\mu m}$ $1/e^2$ waist) of the cavity and show trapping of atoms in higher transverse modes. This work paves the way toward compact, high sensitivity, multi-axis interferometry.Comment: 5 pages, 6 figure

Equivalence Principle and Gravitational Redshift

We investigate leading order deviations from general relativity that violate the Einstein equivalence principle in the gravitational standard model extension. We show that redshift experiments based on matter waves and clock comparisons are equivalent to one another. Consideration of torsion balance tests, along with matter wave, microwave, optical, and M\"ossbauer clock tests, yields comprehensive limits on spin-independent Einstein equivalence principle-violating standard model extension terms at the $10^{-6}$ level.Comment: 4 pages, 1 figure, 2 tables. Detailed synchronization procedure. Accepted in Physical Review Letter

Fractions as Numbers and Extensions of the Number System: Developing Activities Based on Research

Existing studies have shown fractions present significant challenges for K-8 students and pre-service teachers. They suggest that students may fail to see fractions as numbers and have difficulty moving beyond the part-whole realization, and thus they often think of fractions as objects disconnected from the number system. To address this issue, the current study proposes several activities that can be used in mathematics courses for pre-service elementary/secondary teachers or students to help the mrecognize fractions as numbers with the same visual representations as whole numbers (e.g., the number line) and on which the same kinds of operations can be used. Along with a description of the activities,the paper also provides observations about what happened when we gave the activities to a group of 28 prospective elementary teachers, highlighting evidence of their understanding of fractions as numbers