TY - JOUR AU - A. Patscheider AU - L. Chomaz AU - G. Natale AU - D. Petter AU - M. Mark AU - S. Baier AU - B. Yang AU - R. Wang AU - John Bohn AU - F. Ferlaino AB - An accurate knowledge of the scattering length is fundamental in ultracold quantum gas experiments and essential for the characterization of the system as well as for a meaningful comparison to theoretical models. Here, we perform a careful characterization of the s-wave scattering length as for the four highest-abundance isotopes of erbium, in the magnetic field range from 0 to 5 G. 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 rethermalization (NCPR) to obtain as 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 as, 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 us to estimate the number of bound states of erbium. BT - Phys. Rev. A DA - 2022-06 DO - 10.1103/PhysRevA.105.063307 IS - 6 N2 - An accurate knowledge of the scattering length is fundamental in ultracold quantum gas experiments and essential for the characterization of the system as well as for a meaningful comparison to theoretical models. Here, we perform a careful characterization of the s-wave scattering length as for the four highest-abundance isotopes of erbium, in the magnetic field range from 0 to 5 G. 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 rethermalization (NCPR) to obtain as 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 as, 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 us to estimate the number of bound states of erbium. PB - American Physical Society PY - 2022 EP - 063307 T2 - Phys. Rev. A TI - Determination of the scattering length of erbium atoms UR - https://link.aps.org/doi/10.1103/PhysRevA.105.063307 VL - 105 ER -