  In a recent Letter (Phys. Rev. lett. 105, 195301 (2010)), Song et al.
introduced a new variational approach to treat strong attractive boson-fermion
(BF) correlations in BF atomic mixtures. The proposed theory predicts a first
order phase transition to a condensate of composite BF pairs with center of
mass momentum Q=0 as opposed to a composite fermionic molecular Fermi gas. We
show in this comment that their approach is incorrect and moreover, by
resorting to an exactly solvable model we demonstrate that there cannot be more
than one correlated Q=0 BF pair in complete contradiction with their
conclusions.
