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Many-body properties of a fermionic impurity embedded in a Bose-Einsteincondensate are analyzed analytically using a solvable model, theharmonic-interaction model for Bose-Fermi mixtures. The one-particle andtwo-particle densities, reduced density matrices, and correlation functions ofthe fermions and bosons, both in position and momentum spaces, are prescribedin closed form. The various coherence lengths are analyzed. We show that thefirst-order coherence lengths in position and momentum spaces are equal whereasthe second-order quantities can differ substantially. Illustrative exampleswhere the sole interaction is between the impurity and the condensate arepresented. Implications are briefly discussed.

Correlation Effects in a Trapped Bose-Fermi Mixture: Exact Results