In this study, we explore the behavior of a rotating molecular impurity in a two-dimensional Bose-Einstein condensate. Using a Gross-Pitaevskii-type equation, we investigate how the impurity-bath interaction and size of the condensate affect the angular momentum distribution, density deformation, and density currents in the system. In line with experimental results and angulon theory, we show that the impurity's effective moment of inertia is modified by its interaction with the quantum solvent, leading to a slowing down of its rotation for low angular momentum states. Additionally, we observe the emergence of collective excitations such as solitons and vortices in the system after rapid rotation of the impurity. Our model provides insight into the behavior of impurities in two-dimensional quantum gases and can be seen as an effective description of a rotating molecule on the surface of a superfluid helium droplet.

We theoretically investigate the properties of two interacting ultracold highly magnetic atoms trapped in a one-dimensional harmonic potential. The atoms interact via an anisotropic long-range dipole-dipole interaction, which in one dimension effectively can be modeled by the contact interaction. We investigate the interplay of the external magnetic field, the spin-spin interaction, and the trapping potential and how they affect the magnetization of the system. We show the role of indistinguishability and symmetries in the dynamics by studying the time evolution of the observables that could be measured experimentally. The presented model may depict the on-site interaction of the extended Hubbard models, therefore giving a better understanding of the fundamental building block of the respective many-body quantum simulators.