  We consider the problem of a single \down atom in the presence of a Fermi sea
of \up atoms, in the vicinity of a Feshbach resonance. We calculate the
chemical potential and the effective mass of the \down atom using two simple
approaches: a many-body variational wave function and a T-matrix approximation.
These two methods lead to the same results and are in good agreement with
existing quantum Monte-Carlo calculations performed at unitarity and, in one
dimension, with the known exact solution. Surprisingly, our results suggest
that, even at unitarity, the effect of interactions is fairly weak and can be
accurately described using single particle-hole excitations. We also consider
the case of unequal masses.
