Polarons in supersolids: path-integral treatment of an impurity in a one-dimensional dipolar supersolid

The supersolid phase of a dipolar Bose-Einstein condensate has an intriguing excitation spectrum displaying a band structure. Here, the dressing of an impurity in a one-dimensional dipolar supersolid with the excitations of the supersolid is studied. The ground-state energy of the supersolid polaron is calculated using a variational path integral approach, which obtained accurate results for other polaron systems within the Bogoliubov and Fr\"ohlich approximations. A divergence is observed at the superfluid-supersolid phase transition. The polaron radius is also computed, showing that for strong impurity-atom interactions, the polaron can become localized to a single droplet, behaving like a small solid-state polaron.