Dynamics of polaron formation in weakly interacting 1D Bose gases

In recent years much research has been devoted to understand the ground-state properties of Bose polarons, quasiparticles composed of mobile impurities surrounded by a degenerate Bose gas. However, many questions regarding their dynamics remained open. Here we present a detailed study of the time evolution of an impurity injected into a one-dimensional Bose gas, either homogeneous or harmonically trapped. The system is analyzed in a mean-field approach that accounts for the backaction to the condensate and goes beyond the standard Froehlich model, complemented with Truncated Wigner simulations to include quantum fluctuation. We find a rich scenario of dynamical regimes including deceleration or even backscattering caused by the emission of density waves or solitons. Due to the formation of the polaron, the impurity is slowed down even when initially slower than the Landau critical velocity. Under certain conditions the system does not evolve into the polaron ground state, but rather into a metastable excited one, corresponding to the trapping of a soliton at the position of the impurity. We analyze quantum fluctuations in the trapped system and show under what conditions their influence can be made small.