Polaronic Properties of an Ion in a Bose-Einstein Condensate in the Strong-Coupling Limit

Cold atoms can be used to model the Frohlich polaron Hamiltonian using an impurity in a condensate. To probe the strong-coupling regime (which remains elusive in the solid state) charged impurities can be better suited that neutral impurities. However, the ion-atom interaction leads to a stronger depletion of the condensate as compared to the depletion from interaction with neutral impurities, and a good correspondence between the Frohlich Hamiltonian and the cold atom system is only possible when the Bogoliubov approximation is valid. We use a strong-coupling variational approach to estimate an upper limit to the ion-atom coupling strength (expressed through a dimensionless coupling constant). The all-coupling path integral approach is used to estimate the values of the coupling constant that would need to be reached to probe the strong-coupling polaron physics. From these two approaches, we identify a regime where ions in condensates can model strong-coupling polarons and we calculate ground state properties in this regime.