We consider the ground-state properties of an impurity particle (“polaron”) resonantly
interacting with a Bose-Einstein condensate (BEC). Focusing on the equal-mass system,
we use a variational wave function for the polaron that goes beyond previous work and
includes up to three Bogoliubov excitations of the BEC, thus allowing us to capture
both Efimov trimers and associated tetramers. We find that the length scale associated
with Efimov trimers (i.e., the three-body parameter) can strongly affect the polaron’s
behavior, even at densities where there are no well-defined Efimov states. However, by
comparing our results with recent quantum Monte Carlo calculations, we argue that the
polaron energy is a universal function of the Efimov three-body parameter for
sufficiently low boson densities. We further support this conclusion by showing that
the energies of the deepest bound Efimov trimers and tetramers at unitarity are
universally related to one another, regardless of the microscopic model. On the other
hand, we find that the quasiparticle residue and effective mass sensitively depend on
the coherence length