Accurate determination of the scattering length of erbium atoms

TL;DR

This study precisely measures the scattering length of erbium isotopes in ultracold gases using thermalization and spectroscopy, providing new insights into dipolar interactions and isotope properties.

Contribution

It introduces a combined experimental and theoretical approach to accurately determine the scattering length of erbium isotopes, including a model for isotope-dependent background scattering.

Findings

Good agreement between thermalization and spectroscopy methods.

Observed NCPR dependence on density, indicating deviations from ideal trapping.

Estimated the number of bound states of erbium based on isotope data.

Abstract

An accurate knowledge of the scattering length is fundamental in ultracold quantum gas experiments and essential for the characterisation of the system as well as for a meaningful comparison to theoretical models. Here, we perform a careful characterisation of the s-wave scattering length $a_s$ for the four highest-abundance isotopes of erbium, in the magnetic field range from 0G to 5G. We report on cross-dimensional thermalization measurements and apply the Enskog equations of change to numerically simulate the thermalization process and to analytically extract an expression for the so-called number of collisions per re-thermalization (NCPR) to obtain $a_s$ from our experimental data. We benchmark the applied cross-dimensional thermalization technique with the experimentally more demanding lattice modulation spectroscopy and find good agreement for our parameter regime. Our experiments are compatible with a dependence of the NCPR with $a_s$, as theoretically expected in the case of strongly dipolar gases. Surprisingly, we experimentally observe a dependency of the NCPR on the density, which might arise due to deviations from an ideal harmonic trapping configuration. Finally, we apply a model for the dependency of the background scattering length with the isotope mass, allowing to estimate the number of bound states of erbium.