  A single down spin Fermion with an attractive, zero range interaction with a
Fermi sea of up-spin Fermions forms a polaronic quasiparticle. The associated
quasiparticle weight vanishes beyond a critical strength of the attractive
interaction, where a many-body bound state is formed. From a variational
wavefunction in the molecular limit, we determine the critical value for the
polaron to molecule transition. The value agrees well with the diagrammatic
Monte Carlo results of Prokof'ev and Svistunov and is consistent with recent
rf-spectroscopy measurements of the quasiparticle weight by Schirotzek et. al.
In addition, we calculate the contact coefficient of the strongly imbalanced
gas, using the adiabatic theorem of Tan and discuss the implications of the
polaron to molecule transition for the phase diagram of the attractive Fermi
gas at finite imbalance.
