Tools for designing atom interferometers in a microgravity environment

We present a variational model suitable for rapid preliminary design of atom interferometers in a microgravity environment. The model approximates the solution of the 3D rotating--frame Gross--Pitaevskii equation (GPE) as the sum of Nc Gaussian clouds. Each Gaussian cloud is assumed to have time--de...

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Bibliographic Details
Published in:arXiv.org 2019-03
Main Authors: Ashwood, Elizabeth, Wells, Ed Wesley, Kurkcuoglu, Doga Murat, Robert Colson Sapp, Clark, Charles W, Edwards, Mark
Format: Article
Language:English
Subjects:
Atom interferometry
Equations of motion
Error analysis
Error detection
Gravitational constant
Interferometers
Mathematical models
Microgravity
Multinational space ventures
Parameters
Preliminary designs
Three dimensional models
Time dependence
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Summary:We present a variational model suitable for rapid preliminary design of atom interferometers in a microgravity environment. The model approximates the solution of the 3D rotating--frame Gross--Pitaevskii equation (GPE) as the sum of Nc Gaussian clouds. Each Gaussian cloud is assumed to have time--dependent center positions, widths, and linear and quadratic phase parameters. We applied the Lagrangian Variational Method (LVM) with this trial wave function to derive equations of motion for these parameters that can be adapted to any external potential. We also present a 1D version of this variational model. As an example we apply the model to a 1D atom interferometry scheme for measuring Newton's gravitational constant, G, in a microgravity environment. We show how the LVM model can (1) constrain the experimental parameter space size, (2) show how the value of G can be obtained from the experimental conditions and interference pattern characteristics, and (3) show how to improve the sensitivity of the measurement and construct a preliminary error budget.
ISSN:2331-8422
DOI:10.48550/arxiv.1903.04028