# Efficient description of Bose-Einstein condensates in time-dependent rotating traps

## TL;DR

This paper introduces an efficient analytical and numerical approach to model Bose-Einstein condensates in time-dependent rotating traps, aiding high-precision quantum sensing applications.

## Contribution

It presents a novel combined analytical and numerical method for accurately predicting condensate dynamics in complex, time-dependent rotating traps.

## Key findings

- Analytical expressions for spatial and momentum distributions.
- Comparison with previous methods shows improved efficiency.
- Results are directly applicable to experimental quantum sensors.

## Abstract

Quantum sensors based on matter-wave interferometry are promising candidates for high-precision gravimetry and inertial sensing in space. The favorable source for the coherent matter waves in these devices are Bose-Einstein condensates. A reliable prediction of their dynamics, which is governed by the Gross-Pitaevskii equation, requires suitable analytical and numerical methods which take into account the center-of-mass motion of the condensate, its rotation and its spatial expansion by many orders of magnitude. In this chapter, we present an efficient way to study their dynamics in time-dependent rotating traps that meet this objective. Both, an approximate analytical solution for condensates in the Thomas-Fermi regime and dedicated numerical simulations on a variable adapted grid are discussed. We contrast and relate our approach to previous alternative methods and provide further results, such as analytical expressions for the one- and two-dimensional spatial density distributions and the momentum distribution in the long-time limit that are of immediate interest to experimentalists working in this field of research.