Accurate determination of the scattering length of erbium atoms

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 as for the four highest-abundance isotopes of erbium, in the magnetic field range from 0 G 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 re-thermalization (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 to estimate the number of bound states of erbium.

Strongly dipolar gases in a one-dimensional lattice: Bloch oscillations and matter-wave localization

“…1(a). The B-to-as conversion has been precisely mapped out in previous experiments [4,20]. Before loading the lattice, we rotate the magnetic field direction along the y-axis in 50 ms and change its absolute value to set the scattering length.…”

“…Optical lattices enable powerful interferometric approaches to, e.g., measure with high precision the zerocrossing of the scattering length or of the mean-field interaction with the so-called Bloch oscillation (BO) technique [15][16][17][18], and to achieve an accurate determination of the background scattering length via lattice spectroscopy in Hubbard models [4,19,20]. Moreover, the presence of the lattice itself may change completely the phase diagram of the system, as shown in seminal experiments with contact interacting gases [21][22][23].…”

Thermal Conductivity of an Ultracold Paramagnetic Bose Gas

“…In certain cases, the results of this collisional anisotropy are well known. They have already been shown to result in anisotropic thermalization in normal phase ultracold gases, and can be used as a tool for measuring scattering lengths [2][3][4][5][6][7][8][9][10]. These experiments have been modeled using perturbation theory around the equilibrium Boltzmann distribution of a gas, an analysis that has proven highly successful.…”