# Tools for designing atom interferometers in a microgravity environment

## TL;DR

This paper introduces a variational model using Gaussian clouds for rapid design and analysis of atom interferometers in microgravity, aiding in optimizing experiments to measure gravitational constants.

## Contribution

The paper develops a flexible variational model based on Gaussian clouds and applies it to design and optimize atom interferometers in microgravity environments.

## Key findings

- Model constrains experimental parameter space.
- Demonstrates how to extract G from interference patterns.
- Provides methods to improve measurement sensitivity.

## Abstract

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.