Self-localization of a small number of Bose particles in a superfluid Fermi system

We consider self-localization of a small number of Bose particles immersed in a large homogeneous superfluid mixture of fermions in three- and one-dimensional space. Bosons distort the density of surrounding fermions and create a potential well where they can form a bound state analogous to a small polaron state. In the three-dimensional volume, we observe the self-localization for repulsive interactions between bosons and fermions. In the one-dimensional case, bosons self-localize as well for attractive interactions, thereby forming, together with a pair of fermions at the bottom of the Fermi sea, a vector soliton. We analyze also thermal effects and show that small nonzero temperature affects the pairing function of the Fermi subsystem and has little influence on the self-localization phenomena.