Modeling Inelastic Spin-Dependent Scattering in Ultracold Erbium Gas

The large magnetic dipole moment and large orbital angular momentum characteristics of lanthanides such as Erbium introduce complex collisional properties that greatly differ from scattering behavior observed in alkali atoms. In particular, the anisotropic dipole-dipole interactions that result from the large magnetic dipole moment along with the many possible coupling channels present in the collision create a dense spectrum of Feshbach resonances [1]. We present results of a theoretical and computational study of spin-dependent scattering behaviors of ultracold Erbium, focusing in particular on the inelastic spin-exchange (spin-conserving) and spin-relaxation (non-spin-conserving) processes. We specifically analyze the ratios between these two processes to characterize the atom loss from the trap due to spin-relaxation. Excessive loss from spin-relaxation would make the system unstable and present experimental challenges. We use coupled-channel scattering formalism to derive the S-matrix and the resulting cross-section and collisional rate constants for each of these cases as a function of ingoing and outgoing spins, collision energy, and magnetic field. From this study, we aim to understand the microscopic mechanisms underlying these processes; in particular, the characteristics of these interactions that might make one inelastic scattering process more probable than the other one. 

[1] L. Lafforgue et al., arXiv:2512.17556 [cond-mat.quant-gas] (2025).