We investigate the behavior of impurity fields immersed in a larger
condensate field in 1, 2, and 3 dimensions. We discuss the localization of a
single impurity field within a condensate and note the effects of surface
energy. We derive the functional form of the attractive interaction between two
impurities due to mediation from the condensate. Generalizing the analysis to
N impurity fields, we show that within various parameter regimes a crystal of
impurity fields can form spontaneously in the condensate. Finally, the system
of condensate and crystallized impurity structure is shown to have nonclassical
rotational inertia, which is characteristic of superfluidity, i.e. the system
can be seen to exhibit supersolid behavior.Comment: 5 pages, 3 color figures; Accepted to Phys. Rev. Let