Analysis of Powers-of-two Calculations of AVAR and Their Relation to SVAR
N.K. Schlossberger, D. A. Howe
Proceedings of the 2019 Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)
In this work we justify the practice of using the usual powers-of-two values of the Allan variance (AVAR) in determining power law noise types present in recorded data. Its primary merits are that it indicates power-law noise slopes and their levels, including a mixture of these noises. We show that unlike decade values or other arbitrary series, the powers-of-two values are the closest-to-independent set of AVAR values possible, and thus optimally decompose frequencies in such a way as to have the least uncertainty in estimating slopes. We further demonstrate the unique property of this choice by proving the equivalence between the sums of the powers-of-two values of the non-overlapping Allan variance (AVARnono) and two times the value of the standard variance (SVAR).

An Experimental Configuration to Probe for Lorentz Symmetry Violation in Electrons Using Trapped Yb+ Ions
N.K. Schlossberger, P. Richerme
Advanced Journal of Graduate Research 4 (1), 15-33
Since extensions of the standard model have been developed that predict violations of local Lorentz invariance (LLI), precision measurement groups have been working to reduce experimental bounds of the associated matrix element. Using an analogue of the Michelson-Morley test with trapped Ca+ ions, the current bound has been set at one part in 1018. However, by instead using Yb+ ions, which have highly stable electronic states for storing quantum information compared to their counterparts and exhibit enhanced effects of LLI breaking asymmetries, we can push the bounds to one part in 1023. In this article, we outline a configuration for such an experiment and offer solutions to experimental concerns. We develop an algorithm for state creation, manipulation, and measurement that minimizes measurement time and transition uncertainty. We also discuss necessary hardware for trapping and manipulating ions including a vacuum system, a Paul trap and the associated electrode voltage supplies, and an optics system for generating and applying transition pulses. The experiment is specifically designed to utilize the existing ion trap hardware in place at the Richerme lab at Indiana University Bloomington.

High resolution tip-tilt positioning system for a next generation MLL-based x-ray microscope
W. Xu, N. Schlossberger, W. Xu, H. Yan, X. Huang, Y.S. Chu, E. Nazaretski
Measurement Science and Technology 28 (12), 127001
Multilayer Laue lenses (MLLs) are x-ray focusing optics with the potential to focus hard x-rays down to a single nanometer level. In order to achieve point focus, an MLL microscope needs to have the capability to perform tip-tilt motion of MLL optics and to hold the angular position for an extended period of time. In this work, we present a 2D tip-tilt system that can achieve an angular resolution of over 100 microdegree with a working range of 4°,by utilizing a combination of laser interferometer and mini retroreflector. The linear dimensions of the developed system are about 30 mm in all directions, and the thermal dissipation of the system during operation is negligible. Compact design and high angular resolution make the developed system suitable for MLL optics alignment in the next generation of MLL-based x-ray microscopes.

A Proposed Experiment to Test Spin-Dependent Effects Beyond Einstein's Theory of Gravitation: The Pound-Rebka Experiment with Spin
Noah Schlossberger, Tasman Payne et. al.
IU Journal of Undergraduate Research 3 (1), 6-17
Einstein's geometric theory of gravity was constructed in part to explain why test particles in a gravitational field all follow the same trajectory independent of the mass of the particle. However, it is known that point particles in quantum mechanics must all possess at least two properties: mass and angular momentum. Many have speculated that spin-dependent effects in gravity might exist which are not contained in Einstein's theory, yet few experimental tests for such a possibility have ever been conducted. We describe an experiment which is very similar to the famous Pound-Rebka experiment, which used the Mössbauer effect to verify for the first time Einstein’s prediction for the curvature of time, but which employs Mossbauer emitters and absorbers with nonzero spin. We present a specific, realistic proposal for such an experiment. We outline the theory for the “normal” effects of general relativity a la Pound-Rebka, the proposed experimental apparatus including spinpolarized emitters and absorbers, the expected sensitivity of the experiment, and potential sources of systematic error.