Dropping cold quantum gases on Earth over long times and large distances

TL;DR

This paper models the quantum dynamics of ultra-cold gases falling under Earth's gravity over long durations and distances, providing a theoretical framework for drop tower experiments like those by QUANTUS.

Contribution

It develops a quantum field theoretical description of falling ultra-cold gases, including transformations to inertial and non-inertial frames, applicable to long-distance drop experiments.

Findings

Quantum dynamics of Bose-Einstein condensates can be simulated over 100m fall.

Transformations eliminate non-inertial forces, simplifying the analysis.

The approach facilitates numerical studies of long-distance quantum drops.

Abstract

We describe the non-relativistic time evolution of an ultra-cold degenerate quantum gas (bosons/fermions) falling in Earth's gravity during long times (10 sec) and over large distances (100 m). This models a drop tower experiment that is currently performed by the QUANTUS collaboration at ZARM (Bremen, Germany). Starting from the classical mechanics of the drop capsule and a single particle trapped within, we develop the quantum field theoretical description for this experimental situation in an inertial frame, the corotating frame of the Earth, as well as the comoving frame of the drop capsule. Suitable transformations eliminate non-inertial forces, provided all external potentials (trap, gravity) can be approximated with a second order Taylor expansion around the instantaneous trap center. This is an excellent assumption and the harmonic potential theorem applies. As an application, we study the quantum dynamics of a cigar-shaped Bose-Einstein condensate in the Gross-Pitaevskii mean-field approximation. Due to the instantaneous transformation to the rest-frame of the superfluid wave packet, the long-distance drop (100m) can be studied easily on a numerical grid.