Extended mean-field theory of strongly correlated Bose polarons

A paradigmatic class of problems in quantum kinetic theory concerns the physics of mobile quantum impurities immersed in degenerate gases. In a condensed Bose gas, a mobile impurity leads to the formation of a quasiparticle termed Bose polaron, whose characteristics are strongly influenced by many-body effects. In particular, in the presence of an impurity-boson bound state, repulsive interaction among bosons becomes crucial for the system's stability, leading to a strongly correlated phase. We employ a novel variational ansatz to study the ground state of the Bose polaron in three dimensions, accounting for multiple occupations of the bound state and dressing by a coherent state of excitations in the Bose gas. We find that the repulsive inter boson interaction renders the ground state energy finite across a Feshbach resonance. For positive scattering lengths, a transition occurs when a single boson forms a bound state with the impurity at a scattering length significantly larger than the one predicted by non-interacting mean-field theory for the transition between attractive and repulsive polaron. Our ansatz can be readily extended to lower dimensions where the effect of quantum fluctuations becomes more prominent and to non-equilibrium settings to study the dynamics of Bose polaron formation.