Phase diagram and dynamics of magnetic Bose polarons

We investigate the nonequilibrium dynamics of magnetic polarons by considering an impurity atom dressed by spin-wave excitations in a one-dimensional spinor Bose gas. The phase diagram which contains self-bound and repulsive magnetic polarons as well as phase-separated regime is obtained as a function of Rabi-coupling and spin-spin interactions. A waveform of the magnetic polaron is extracted through an effective model. The residue is found to drop for strong impurity-spin interactions towards the polaron catastrophe. We infer the dynamical persistence of the respective repulsive and attractive branches associated with the generation of strongly correlated spin-waves. Strikingly, a dynamical decay at early stages of the dynamics is observed for strong impurity-medium interactions followed by a diffusive polaron behavior. The impurity can be utilized to probe and manipulate spin-demixing by suppressing ferromagnetic spin-spin correlations. Controllable spin-demixing and correlated magnetic polarons are experimentally realizable with current technologies.