# Rotational cooling of molecules in a Bose-Einstein-Condensate

## TL;DR

This paper explores how diatomic molecules cool rotationally within a Bose-Einstein condensate through phonon emission, revealing conditions for suppressed emission and analyzing the dynamics of angulon quasiparticles.

## Contribution

It introduces a detailed analysis of rotational cooling mechanisms in BECs, including the effects of molecule size and thermal phonons, and discusses the finite lifetime of angulons.

## Key findings

- Rotational relaxation is generally faster than linear impurity cooling in BECs.
- Suppression of phonon emission occurs below a critical angular momentum for macro-dimers.
- Finite lifetime of angulons due to phonon interactions is characterized.

## Abstract

We discuss the rotational cooling of diatomic molecules in a Bose-Einstein condensate (BEC) of ultra-cold atoms by emission of phonons with orbital angular momentum. Despite the superfluidity of the BEC there is no frictionless rotation for typical molecules since the dominant cooling occurs via emission of particle-like phonons. Only for macro-dimers, whose size becomes comparable or larger than the condensate healing length, a Landau-like, critical angular momentum exists below which phonon emission is suppressed. We find that the rotational relaxation of typical molecules is in general faster than the cooling of the linear motion of impurities in a BEC. This also leads to a finite lifetime of angulons, quasi-particles of rotating molecules coupled to phonons with orbital angular-momentum. We analyze the dynamics of rotational cooling for homo-nuclear diatomic molecules based on a quantum Boltzmann equation including single- and two-phonon scattering and discuss the effect of thermal phonons.