Rapidity and momentum distributions of one-dimensional dipolar quantum gases

We explore the effect of tunable integrability-breaking dipole-dipole interactions in the equilibrium states of highly magnetic one-dimensional (1D) Bose gases of dysprosium at low temperatures. We experimentally observe that in the strongly correlated Tonks-Girardeau regime, rapidity and momentum distributions are nearly unaffected by the dipolar interactions. By contrast, we also observe that significant changes of these distributions occur when decreasing the strength of the contact interactions. We show that the main experimental observations are captured by modeling the system as an array of 1D gases with only contact interactions, dressed by the contribution of the short-range part of the dipolar interactions. Improvements to theory-experiment correspondence will require different tools tailored to near-integrable models possessing both short- and long-range interactions.